id
string | setting_key
string | difficulty
string | level
int32 | messages
dict | ground_truth
string | dataset
string | omega_split
string |
|---|---|---|---|---|---|---|---|
math_algebra_func_area_level_4_4_400
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 1|(-4(4((-3(-2e^(-2x) + 2) + 2)/(-3(-2e^(-2x) + 2) + 2)) + 5) + 2) - 3| - 2 and g(x) = 1(-3|(3cos(3π(-1x - 2) + 3)) + 1| - 3)^2 + 2(-3|(3cos(3π(-1x - 2) + 3)) + 1| - 3) - 1 between the vertical lines x = -0.5 and x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
28.7
|
math
|
train
|
math_algebra_func_area_level_4_4_401
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 5(-3sin(1π(-3|(-2|(-3|x + 2|) - 1| - 2) - 3| - 1) + 1) - 2)^2 + 3(-3sin(1π(-3|(-2|(-3|x + 2|) - 1| - 2) - 3| - 1) + 1) - 2) - 5, g(x) = 2cos(1π((-1((2(-3x^2 - 4x + 1) + 2)/(-3(-3x^2 - 4x + 1) - 3)) + 3)/(1((2(-3x^2 - 4x + 1) + 2)/(-3(-3x^2 - 4x + 1) - 3)) + 3)) - 2) - 1, x = 4.9, and x = 5.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.2
|
math
|
train
|
math_algebra_func_area_level_4_4_402
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -1|((2((-3(-5(-1sin(2πx - 2) + 2) - 3) - 2)/(-3(-5(-1sin(2πx - 2) + 2) - 3) - 3)) + 1)/(-1((-3(-5(-1sin(2πx - 2) + 2) - 3) - 2)/(-3(-5(-1sin(2πx - 2) + 2) - 3) - 3)) + 2)) + 2| + 1 and g(x) = 2((-3(-3sin(2π(-3|x - 2| + 3)) + 1) - 3)/(3(-3sin(2π(-3|x - 2| + 3)) + 1))) + 3 between the vertical lines x = -0.7 and x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.6
|
math
|
train
|
math_algebra_func_area_level_4_4_403
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-2((2(-4(2|(5x^2 - 3) + 2| + 1)^2 + 3(2|(5x^2 - 3) + 2| + 1) + 3))/(-2(-4(2|(5x^2 - 3) + 2| + 1)^2 + 3(2|(5x^2 - 3) + 2| + 1) + 3) + 3)))/(-2((2(-4(2|(5x^2 - 3) + 2| + 1)^2 + 3(2|(5x^2 - 3) + 2| + 1) + 3))/(-2(-4(2|(5x^2 - 3) + 2| + 1)^2 + 3(2|(5x^2 - 3) + 2| + 1) + 3) + 3)) - 1) and g(x) = -3(-1sin(1π((-3((2x - 2)/(-3x + 4)))/(-1((2x - 2)/(-3x + 4)) - 2)) - 3) - 1) - 4 from x = -0.5 to x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.9
|
math
|
train
|
math_algebra_func_area_level_4_4_404
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -3|((-3((-2(-1((-2x + 3)/(2x + 3)) + 1) + 1)/(-3(-1((-2x + 3)/(2x + 3)) + 1) - 1)) - 2)/(1((-2(-1((-2x + 3)/(2x + 3)) + 1) + 1)/(-3(-1((-2x + 3)/(2x + 3)) + 1) - 1)) - 3))| - 1 and g(x) = -1|(-3(4(-1x^2 - 3x + 4)^2 + 3(-1x^2 - 3x + 4) + 2) - 1) + 1| - 2 from x = -0.3 to x = -0.19999999999999998. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
29.5
|
math
|
train
|
math_algebra_func_area_level_4_4_405
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -1|(-1cos(3π(3((-1(-1x - 1) + 2)/(-3(-1x - 1) + 4))^2 - 2((-1(-1x - 1) + 2)/(-3(-1x - 1) + 4)) - 1) - 2) - 3)| + 3, g(x) = (1(-1(-3cos(1π(-4x^2 - 5x + 3) - 1))^2 - 2(-3cos(1π(-4x^2 - 5x + 3) - 1)) + 2) + 2)/(2(-1(-3cos(1π(-4x^2 - 5x + 3) - 1))^2 - 2(-3cos(1π(-4x^2 - 5x + 3) - 1)) + 2) + 3), x = 1.7, and x = 1.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.0
|
math
|
train
|
math_algebra_func_area_level_4_4_406
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -1|((3(-4(1((-1x + 2)/(-2x))^2 + 4((-1x + 2)/(-2x)) + 1)^2 - 5(1((-1x + 2)/(-2x))^2 + 4((-1x + 2)/(-2x)) + 1) + 1) + 3)/(1(-4(1((-1x + 2)/(-2x))^2 + 4((-1x + 2)/(-2x)) + 1)^2 - 5(1((-1x + 2)/(-2x))^2 + 4((-1x + 2)/(-2x)) + 1) + 1) + 2)) - 2|, g(x) = (-3(-1(5(3x^2 + 2x + 4)^2 - 5(3x^2 + 2x + 4) + 1) + 1) + 3)/(3(-1(5(3x^2 + 2x + 4)^2 - 5(3x^2 + 2x + 4) + 1) + 1) - 1), x = 0.3, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.5
|
math
|
train
|
math_algebra_func_area_level_4_4_407
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 2|(-5((1(-2((2x)/(2x))^2 + 2((2x)/(2x)) + 4) - 2)/(1(-2((2x)/(2x))^2 + 2((2x)/(2x)) + 4) - 2))^2) - 1| and g(x) = (-1(-2(-3cos(1π(1|x - 2| + 2) - 1) + 1) + 4) + 2)/(2(-2(-3cos(1π(1|x - 2| + 2) - 1) + 1) + 4) + 1) from x = -3.7 to x = -3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
10.4
|
math
|
train
|
math_algebra_func_area_level_4_4_408
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 5((1(4(-3(-3e^(2x) - 3)^2 - 1(-3e^(2x) - 3))^2 - 1(-3(-3e^(2x) - 3)^2 - 1(-3e^(2x) - 3)) - 5) - 1)/(3(4(-3(-3e^(2x) - 3)^2 - 1(-3e^(2x) - 3))^2 - 1(-3(-3e^(2x) - 3)^2 - 1(-3e^(2x) - 3)) - 5) + 1))^2 - 2((1(4(-3(-3e^(2x) - 3)^2 - 1(-3e^(2x) - 3))^2 - 1(-3(-3e^(2x) - 3)^2 - 1(-3e^(2x) - 3)) - 5) - 1)/(3(4(-3(-3e^(2x) - 3)^2 - 1(-3e^(2x) - 3))^2 - 1(-3(-3e^(2x) - 3)^2 - 1(-3e^(2x) - 3)) - 5) + 1)) and g(x) = 2(4(-2(-3x^2 - 1x + 5)^2 + 2(-3x^2 - 1x + 5) + 2)^2 - 5) + 1 from x = 1.0 to x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
5.3
|
math
|
train
|
math_algebra_func_area_level_4_4_409
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -5(-1(-2(1(-3|x + 3| - 2) + 4)^2 + 4(1(-3|x + 3| - 2) + 4)) - 2) + 3, g(x) = 2|(2sin(3π(2|(-2|x + 1| + 2) + 3| - 1) - 1) - 1) - 3| - 3, x = -2.3, and x = -2.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_4_4_410
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 1(-2(1|(3((1x)/(1x + 3)) + 5)| + 2)^2 - 4(1|(3((1x)/(1x + 3)) + 5)| + 2) + 4) - 2, g(x) = -3|(3|(-1cos(1π(-1x - 2) + 3) - 1) - 1| + 2)| - 1, x = -1.9, and x = -1.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_4_4_411
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -5((3(3|((3(4x^2 - 1x - 3) + 1)/(1(4x^2 - 1x - 3))) + 3| - 3) - 1)/(-3(3|((3(4x^2 - 1x - 3) + 1)/(1(4x^2 - 1x - 3))) + 3| - 3) + 4)) - 2, g(x) = (2(2cos(2π(3(-3x - 1) - 3) - 1) + 3))/(-2(2cos(2π(3(-3x - 1) - 3) - 1) + 3) + 3), x = -0.4, and x = -0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.3
|
math
|
train
|
math_algebra_func_area_level_4_4_412
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -2(-4(2(2|(-2e^(1x) + 2) - 1| - 1)^2 - 3(2|(-2e^(1x) + 2) - 1| - 1) + 3) + 5)^2 - 3(-4(2(2|(-2e^(1x) + 2) - 1| - 1)^2 - 3(2|(-2e^(1x) + 2) - 1| - 1) + 3) + 5) + 1 and g(x) = -1(5((-2(-2|x + 2| + 2) + 2)/(-2(-2|x + 2| + 2) + 3)) + 4)^2 - 5(5((-2(-2|x + 2| + 2) + 2)/(-2(-2|x + 2| + 2) + 3)) + 4) - 2 from x = -0.3 to x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
35.3
|
math
|
train
|
math_algebra_func_area_level_4_4_413
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1(1sin(2π(-5(4(2|x + 1| + 2) + 5) - 3) + 1) + 3) + 4 and g(x) = 3|(-2(3|(1x^2 + 2x + 1)| - 3)^2 + 3(3|(1x^2 + 2x + 1)| - 3) + 3)| - 1 from x = 0.3 to x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.5
|
math
|
train
|
math_algebra_func_area_level_4_4_414
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -2(3|((1(5(2|x + 3| + 1)^2 - 5(2|x + 3| + 1)))/(3(5(2|x + 3| + 1)^2 - 5(2|x + 3| + 1)) - 1)) - 3| + 3) + 4 and g(x) = -1(-2(-2(1x^2 + 1x + 2) + 4)^2 - 4(-2(1x^2 + 1x + 2) + 4) + 1)^2 + 4(-2(-2(1x^2 + 1x + 2) + 4)^2 - 4(-2(1x^2 + 1x + 2) + 4) + 1) - 5 from x = -1.8 to x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
33.7
|
math
|
train
|
math_algebra_func_area_level_4_4_415
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 3(-3cos(1π(4(-5((3x + 2)/(-3x - 3)) - 4) + 5)) - 2) + 3 and g(x) = (3(2(5(3|x - 2| - 2) - 1)^2 - 1(5(3|x - 2| - 2) - 1) - 2))/(3(2(5(3|x - 2| - 2) - 1)^2 - 1(5(3|x - 2| - 2) - 1) - 2) + 1) between the vertical lines x = -1.2 and x = -1.0999999999999999. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.6
|
math
|
train
|
math_algebra_func_area_level_4_4_416
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -2|(-2((1(1|(1x + 4) - 2| + 3) - 3)/(2(1|(1x + 4) - 2| + 3) + 2)) - 3) - 1| + 1 and g(x) = (-2(4((-1((3x)/(-3x + 2)) + 3)/(2((3x)/(-3x + 2)) + 1))^2 - 4) + 3)/(3(4((-1((3x)/(-3x + 2)) + 3)/(2((3x)/(-3x + 2)) + 1))^2 - 4) - 1) between the vertical lines x = 0.3 and x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4.0
|
math
|
train
|
math_algebra_func_area_level_4_4_417
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 2sin(1π(4((3(2(2|x| + 1)^2 - 4(2|x| + 1) + 4) + 2)/(-2(2(2|x| + 1)^2 - 4(2|x| + 1) + 4) - 1)) + 2)) - 1, g(x) = -1|(-4(1|((1x + 1)/(3x)) - 2| - 1) - 1) + 2|, x = 0.2, and x = 0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_4_4_418
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -3|(3(2cos(1π((2(-4x^2))/(3(-4x^2) + 1))) - 2) + 3) - 3| + 2 and g(x) = 1|(-1|(2sin(3π(-2|x| - 3) + 2) + 2) - 2| + 2) - 2| from x = 0.0 to x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.0
|
math
|
train
|
math_algebra_func_area_level_4_4_419
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-1(3(-2(2(-2x + 5) - 5) + 5)^2 + 5))/(1(3(-2(2(-2x + 5) - 5) + 5)^2 + 5) + 3), g(x) = -3|(4((3(4x^2 - 2x - 4) + 1)/(-2(4x^2 - 2x - 4) - 2)) - 1) - 3| + 3, x = 1.2, and x = 1.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.9
|
math
|
train
|
math_algebra_func_area_level_4_4_420
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (-3(-1sin(2π(-4(1|(-1|x + 2| + 2) + 1| + 3)^2 + 3(1|(-1|x + 2| + 2) + 1| + 3)) - 1) - 1) + 3)/(1(-1sin(2π(-4(1|(-1|x + 2| + 2) + 1| + 3)^2 + 3(1|(-1|x + 2| + 2) + 1| + 3)) - 1) - 1) + 1) and g(x) = 1(-2cos(1π((-1(-5x^2 - 5x - 2))/(-2(-5x^2 - 5x - 2) - 3)) + 1) - 2)^2 + 2(-2cos(1π((-1(-5x^2 - 5x - 2))/(-2(-5x^2 - 5x - 2) - 3)) + 1) - 2) - 2 between the vertical lines x = -0.5 and x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.0
|
math
|
train
|
math_algebra_func_area_level_4_4_421
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (2((3(2(1((1x + 3)/(3x + 1)))^2 - 4(1((1x + 3)/(3x + 1))) + 1) + 3)/(1(2(1((1x + 3)/(3x + 1)))^2 - 4(1((1x + 3)/(3x + 1))) + 1) + 1)))/(2((3(2(1((1x + 3)/(3x + 1)))^2 - 4(1((1x + 3)/(3x + 1))) + 1) + 3)/(1(2(1((1x + 3)/(3x + 1)))^2 - 4(1((1x + 3)/(3x + 1))) + 1) + 1)) - 1) and g(x) = 2((-1((3(-3sin(3πx) - 2) + 1)/(1(-3sin(3πx) - 2))) + 2)/(-2((3(-3sin(3πx) - 2) + 1)/(1(-3sin(3πx) - 2))) - 1)) + 1 between the vertical lines x = -4.4 and x = -4.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_4_4_422
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -3sin(2π(-2(1(5(-3x^2 + 3x + 4)^2 + 5(-3x^2 + 3x + 4) - 1)^2 + 2(5(-3x^2 + 3x + 4)^2 + 5(-3x^2 + 3x + 4) - 1) + 5)^2 + 1(1(5(-3x^2 + 3x + 4)^2 + 5(-3x^2 + 3x + 4) - 1)^2 + 2(5(-3x^2 + 3x + 4)^2 + 5(-3x^2 + 3x + 4) - 1) + 5) - 2) - 2) - 2 and g(x) = -2|((1(2e^(1(-3|x| - 2)) - 2) + 3)/(-3(2e^(1(-3|x| - 2)) - 2) - 2)) - 2| between the vertical lines x = -0.7 and x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_4_4_423
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -5((1((1(-1cos(1π(4x^2 + 4x + 4) + 3) + 2) + 3)/(-1(-1cos(1π(4x^2 + 4x + 4) + 3) + 2) + 2)) - 3)/(-2((1(-1cos(1π(4x^2 + 4x + 4) + 3) + 2) + 3)/(-1(-1cos(1π(4x^2 + 4x + 4) + 3) + 2) + 2)) - 2))^2 + 3((1((1(-1cos(1π(4x^2 + 4x + 4) + 3) + 2) + 3)/(-1(-1cos(1π(4x^2 + 4x + 4) + 3) + 2) + 2)) - 3)/(-2((1(-1cos(1π(4x^2 + 4x + 4) + 3) + 2) + 3)/(-1(-1cos(1π(4x^2 + 4x + 4) + 3) + 2) + 2)) - 2)) + 1, g(x) = -1|(-5(4(5x^2 - 2x - 3) + 5) + 3) - 3| - 3, x = 0.8, and x = 0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.5
|
math
|
train
|
math_algebra_func_area_level_4_4_424
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-2(2|((3(-1|(1sin(2πx - 1) + 2)| - 1) - 1)/(1(-1|(1sin(2πx - 1) + 2)| - 1))) + 3|) - 2)/(2(2|((3(-1|(1sin(2πx - 1) + 2)| - 1) - 1)/(1(-1|(1sin(2πx - 1) + 2)| - 1))) + 3|) + 2), g(x) = -2(1(-3cos(3π(-2|x + 3| + 1) - 3) - 2)^2 + 3(-3cos(3π(-2|x + 3| + 1) - 3) - 2) + 4) + 3, x = 1.8, and x = 1.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.8
|
math
|
train
|
math_algebra_func_area_level_4_4_425
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -2(4((1(1|(-1sin(1πx + 1) + 3) + 2| + 3) - 2)/(-3(1|(-1sin(1πx + 1) + 3) + 2| + 3) - 2))) + 4 and g(x) = 3|((-2(1|(-5x^2 + 3x + 5) + 1| - 2) + 1)/(3(1|(-5x^2 + 3x + 5) + 1| - 2) + 1))| - 2 between the vertical lines x = -0.7 and x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
5.9
|
math
|
train
|
math_algebra_func_area_level_4_4_426
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -4(-3|(-3sin(3π((3(-1|x| + 1) + 2)/(1(-1|x| + 1) - 3)) + 3) + 2) + 1| + 3) + 5, g(x) = 3(5(-3(-2|x + 3|) - 4)^2 + 3(-3(-2|x + 3|) - 4) + 5) + 2, x = -3.6, and x = -3.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.9
|
math
|
train
|
math_algebra_func_area_level_4_4_427
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (1(-4((-2(-2(1|x| - 2) + 1) - 1)/(3(-2(1|x| - 2) + 1) - 2))^2 - 5((-2(-2(1|x| - 2) + 1) - 1)/(3(-2(1|x| - 2) + 1) - 2)) - 1) + 3)/(-1(-4((-2(-2(1|x| - 2) + 1) - 1)/(3(-2(1|x| - 2) + 1) - 2))^2 - 5((-2(-2(1|x| - 2) + 1) - 1)/(3(-2(1|x| - 2) + 1) - 2)) - 1)) and g(x) = 2(4((3((1x + 3)/(-1x + 2)) - 3)/(1((1x + 3)/(-1x + 2)) - 2))^2 - 4((3((1x + 3)/(-1x + 2)) - 3)/(1((1x + 3)/(-1x + 2)) - 2)) - 3) + 3 between the vertical lines x = 1.0 and x = 3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
161.5
|
math
|
train
|
math_algebra_func_area_level_4_4_428
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -3(-1(-1cos(1π(2|((-2x + 2)/(-2x + 3)) + 3|) + 2) - 3) - 5)^2 + 1 and g(x) = -5(-1sin(1π(1(-4x^2 + 1x + 5)^2 + 2(-4x^2 + 1x + 5) + 2)) + 3)^2 + 2(-1sin(1π(1(-4x^2 + 1x + 5)^2 + 2(-4x^2 + 1x + 5) + 2)) + 3) - 4 from x = 3.3 to x = 3.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.3
|
math
|
train
|
math_algebra_func_area_level_4_4_429
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -1((1(-3(1(2|x + 1| - 3) - 1)^2 + 2(1(2|x + 1| - 3) - 1) - 3) + 2)/(1(-3(1(2|x + 1| - 3) - 1)^2 + 2(1(2|x + 1| - 3) - 1) - 3) - 3))^2 - 2((1(-3(1(2|x + 1| - 3) - 1)^2 + 2(1(2|x + 1| - 3) - 1) - 3) + 2)/(1(-3(1(2|x + 1| - 3) - 1)^2 + 2(1(2|x + 1| - 3) - 1) - 3) - 3)) + 3 and g(x) = -4(-1(-5(-2cos(1πx + 3))^2 - 3(-2cos(1πx + 3))) - 2) + 1 between the vertical lines x = -1.3 and x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
18.8
|
math
|
train
|
math_algebra_func_area_level_4_4_430
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-1(-1(3cos(3π(2((-2x)/(3x + 3)) + 3) + 1))) + 3)/(-1(-1(3cos(3π(2((-2x)/(3x + 3)) + 3) + 1))) - 2), g(x) = -1|(2((2(-5x^2 + 2x - 5) - 1)/(2(-5x^2 + 2x - 5) - 1)) - 5) + 2| + 1, x = -1.0, and x = -0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.9
|
math
|
train
|
math_algebra_func_area_level_4_4_431
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-1(3|(1(1((-3x - 2)/(3x - 2))^2 + 5((-3x - 2)/(3x - 2)) - 3)^2 + 4(1((-3x - 2)/(3x - 2))^2 + 5((-3x - 2)/(3x - 2)) - 3) - 3)| - 2))/(-3(3|(1(1((-3x - 2)/(3x - 2))^2 + 5((-3x - 2)/(3x - 2)) - 3)^2 + 4(1((-3x - 2)/(3x - 2))^2 + 5((-3x - 2)/(3x - 2)) - 3) - 3)| - 2) - 3) and g(x) = -2(-3|(4((-3x - 1)/(-3x))^2 + 2((-3x - 1)/(-3x))) - 3| + 1) + 2 from x = -0.2 to x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.1
|
math
|
train
|
math_algebra_func_area_level_4_4_432
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (1((-3((3(-1|(1|x - 3| - 3) - 1| + 1) + 1)/(1(-1|(1|x - 3| - 3) - 1| + 1) + 3)) - 1)/(3((3(-1|(1|x - 3| - 3) - 1| + 1) + 1)/(1(-1|(1|x - 3| - 3) - 1| + 1) + 3)) + 2)) - 3)/(1((-3((3(-1|(1|x - 3| - 3) - 1| + 1) + 1)/(1(-1|(1|x - 3| - 3) - 1| + 1) + 3)) - 1)/(3((3(-1|(1|x - 3| - 3) - 1| + 1) + 1)/(1(-1|(1|x - 3| - 3) - 1| + 1) + 3)) + 2)) - 3) and g(x) = -1|(-4(-3|(-1x^2 - 5x) - 1| + 3)^2 - 5(-3|(-1x^2 - 5x) - 1| + 3)) + 1| + 2 between the vertical lines x = -0.4 and x = -0.30000000000000004. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.9
|
math
|
train
|
math_algebra_func_area_level_4_4_433
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -3(1(1(-3|(-4x - 2) + 3|)^2 + 4(-3|(-4x - 2) + 3|) - 1) - 5) + 5, g(x) = 5(-4(-3(3sin(2πx + 3) - 1) + 3) - 3)^2 + 4, x = 0.6, and x = 0.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
10.8
|
math
|
train
|
math_algebra_func_area_level_4_4_434
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-2(3sin(3π((2(1(1x - 1)^2 - 4(1x - 1) + 3) - 3)/(2(1(1x - 1)^2 - 4(1x - 1) + 3) - 1)) - 2) + 1) - 1)/(-3(3sin(3π((2(1(1x - 1)^2 - 4(1x - 1) + 3) - 3)/(2(1(1x - 1)^2 - 4(1x - 1) + 3) - 1)) - 2) + 1) + 1) and g(x) = (-3(-1(2(3cos(1πx + 2) + 2)^2 + 3(3cos(1πx + 2) + 2) + 3)^2 + 4(2(3cos(1πx + 2) + 2)^2 + 3(3cos(1πx + 2) + 2) + 3) - 3))/(1(-1(2(3cos(1πx + 2) + 2)^2 + 3(3cos(1πx + 2) + 2) + 3)^2 + 4(2(3cos(1πx + 2) + 2)^2 + 3(3cos(1πx + 2) + 2) + 3) - 3)) from x = 3.9 to x = 4.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.4
|
math
|
train
|
math_algebra_func_area_level_4_4_435
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -2((1(2sin(2π(3|((-1x + 1)/(-1x - 1)) + 3| - 2) + 2) + 3) - 1)/(-1(2sin(2π(3|((-1x + 1)/(-1x - 1)) + 3| - 2) + 2) + 3))) and g(x) = 2cos(3π((2(-4(-2x + 4) - 5) - 2)/(-2(-4(-2x + 4) - 5) - 2)) - 3) + 3 from x = 2.4 to x = 3.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.0
|
math
|
train
|
math_algebra_func_area_level_4_4_436
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -4(-5((2(2((2x)/(2x - 1)) + 2) + 2)/(-2(2((2x)/(2x - 1)) + 2) + 3)) - 4) + 5 and g(x) = 2cos(3π(1(2(1|x + 1| - 2)^2 + 3(1|x + 1| - 2) - 3)^2 - 5(2(1|x + 1| - 2)^2 + 3(1|x + 1| - 2) - 3) - 4)) from x = 0.5 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_4_4_437
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 1(1(5(-2(3x)^2 - 3(3x) + 5)^2 - 5(-2(3x)^2 - 3(3x) + 5) - 3)^2 + 1(5(-2(3x)^2 - 3(3x) + 5)^2 - 5(-2(3x)^2 - 3(3x) + 5) - 3) - 4) + 5 and g(x) = (-2(4(5(5x^2 + 2x + 3)^2 - 4(5x^2 + 2x + 3) + 3)^2 + 3(5(5x^2 + 2x + 3)^2 - 4(5x^2 + 2x + 3) + 3) + 1) + 2)/(-2(4(5(5x^2 + 2x + 3)^2 - 4(5x^2 + 2x + 3) + 3)^2 + 3(5(5x^2 + 2x + 3)^2 - 4(5x^2 + 2x + 3) + 3) + 1) + 3) between the vertical lines x = -0.8 and x = -0.7000000000000001. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4.8
|
math
|
train
|
math_algebra_func_area_level_4_4_438
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-1(-2|(-1|(-4(3|x - 1| - 2)^2 - 4(3|x - 1| - 2) + 3) - 2|) + 2| + 2) + 2)/(-3(-2|(-1|(-4(3|x - 1| - 2)^2 - 4(3|x - 1| - 2) + 3) - 2|) + 2| + 2) - 3) and g(x) = (3(3|(3|((2x - 2)/(-1x + 2)) - 1|) + 1| - 1) + 1)/(1(3|(3|((2x - 2)/(-1x + 2)) - 1|) + 1| - 1)) from x = 1.8 to x = 1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.7
|
math
|
train
|
math_algebra_func_area_level_4_4_439
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 1|(-1(-3e^(-2(-3|(-5x^2 + 3x + 5) + 3| + 3)) + 2) - 3) - 3| and g(x) = 1(4(1(-1x^2 + 2)^2 - 4(-1x^2 + 2) - 1)^2 - 5(1(-1x^2 + 2)^2 - 4(-1x^2 + 2) - 1) + 4) + 2 between the vertical lines x = -1.1 and x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
16.6
|
math
|
train
|
math_algebra_func_area_level_4_4_440
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 4((2(-2((2(-4x^2 - 1x + 4) + 2)/(3(-4x^2 - 1x + 4) + 1))^2 + 5((2(-4x^2 - 1x + 4) + 2)/(3(-4x^2 - 1x + 4) + 1)) + 1) - 2)/(-3(-2((2(-4x^2 - 1x + 4) + 2)/(3(-4x^2 - 1x + 4) + 1))^2 + 5((2(-4x^2 - 1x + 4) + 2)/(3(-4x^2 - 1x + 4) + 1)) + 1) + 4))^2 + 1((2(-2((2(-4x^2 - 1x + 4) + 2)/(3(-4x^2 - 1x + 4) + 1))^2 + 5((2(-4x^2 - 1x + 4) + 2)/(3(-4x^2 - 1x + 4) + 1)) + 1) - 2)/(-3(-2((2(-4x^2 - 1x + 4) + 2)/(3(-4x^2 - 1x + 4) + 1))^2 + 5((2(-4x^2 - 1x + 4) + 2)/(3(-4x^2 - 1x + 4) + 1)) + 1) + 4)) - 3, g(x) = 1(-3|((3((-1x - 2)/(1x + 3)) - 3)/(1((-1x - 2)/(1x + 3)))) - 2| + 1)^2 + 1(-3|((3((-1x - 2)/(1x + 3)) - 3)/(1((-1x - 2)/(1x + 3)))) - 2| + 1) - 2, x = -2.9, and x = -2.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_4_4_441
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 2|((2((-1(-4(-5x^2 + 5) + 1) - 3)/(2(-4(-5x^2 + 5) + 1) + 3)) + 3)/(2((-1(-4(-5x^2 + 5) + 1) - 3)/(2(-4(-5x^2 + 5) + 1) + 3)) + 3)) + 3| + 3 and g(x) = 2|(2((3(2|x - 2| - 1) + 3)/(3(2|x - 2| - 1) - 2))^2 + 5((3(2|x - 2| - 1) + 3)/(3(2|x - 2| - 1) - 2)) + 5) + 2| + 1 from x = 1.7 to x = 2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.2
|
math
|
train
|
math_algebra_func_area_level_4_4_442
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 2|((3(1|((-1(2cos(2πx + 2) - 3) - 1)/(-1(2cos(2πx + 2) - 3) + 2)) - 1| + 2) - 3)/(-2(1|((-1(2cos(2πx + 2) - 3) - 1)/(-1(2cos(2πx + 2) - 3) + 2)) - 1| + 2) - 2)) - 1| + 1, g(x) = 1|(5((3(2|x - 1| - 2))/(-3(2|x - 1| - 2) - 3)) - 3) + 2| - 2, x = 0.3, and x = 1.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
141.2
|
math
|
train
|
math_algebra_func_area_level_4_4_443
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-1((3(3(3(-1x^2 - 4x - 5) + 5) + 5))/(2(3(3(-1x^2 - 4x - 5) + 5) + 5) + 3)) - 1)/(2((3(3(3(-1x^2 - 4x - 5) + 5) + 5))/(2(3(3(-1x^2 - 4x - 5) + 5) + 5) + 3)) - 3), g(x) = (-1(-1(1cos(1π(1x^2 + 5x - 1) - 2) - 2)^2 + 2(1cos(1π(1x^2 + 5x - 1) - 2) - 2) + 2) + 2)/(1(-1(1cos(1π(1x^2 + 5x - 1) - 2) - 2)^2 + 2(1cos(1π(1x^2 + 5x - 1) - 2) - 2) + 2)), x = -3.2, and x = -0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
13.9
|
math
|
train
|
math_algebra_func_area_level_4_4_444
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 1|((-2(-1|(-3|(-3x + 3) - 1| - 3) + 3| - 2))/(-1(-1|(-3|(-3x + 3) - 1| - 3) + 3| - 2) - 2)) - 2| and g(x) = -3(2cos(1π(-5((-2x - 3)/(1x))) - 1)) + 1 between the vertical lines x = -1.6 and x = -1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.4
|
math
|
train
|
math_algebra_func_area_level_4_4_445
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1(1(3|((1((-3x + 3)/(2x + 1)) - 1)/(-1((-3x + 3)/(2x + 1)) - 1)) - 2| + 1) - 4)^2 - 2(1(3|((1((-3x + 3)/(2x + 1)) - 1)/(-1((-3x + 3)/(2x + 1)) - 1)) - 2| + 1) - 4) + 4 and g(x) = 1|((-2((1(-1|x|) - 2)/(-1(-1|x|) - 3)) - 2)/(1((1(-1|x|) - 2)/(-1(-1|x|) - 3))))| from x = 0.6 to x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_4_4_446
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -3(-3(-1(2|(-1x^2 - 5x + 5) + 1| - 1) + 2)^2 + 4(-1(2|(-1x^2 - 5x + 5) + 1| - 1) + 2) + 1) + 4 and g(x) = -2e^(1(1(-3(4x - 2) - 3))) + 1 from x = 0.8 to x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_4_4_447
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 2((1(-4(1((1x - 1)/(2x - 3)) + 2)^2 - 4(1((1x - 1)/(2x - 3)) + 2) + 2) - 2)/(1(-4(1((1x - 1)/(2x - 3)) + 2)^2 - 4(1((1x - 1)/(2x - 3)) + 2) + 2) + 1))^2 - 3((1(-4(1((1x - 1)/(2x - 3)) + 2)^2 - 4(1((1x - 1)/(2x - 3)) + 2) + 2) - 2)/(1(-4(1((1x - 1)/(2x - 3)) + 2)^2 - 4(1((1x - 1)/(2x - 3)) + 2) + 2) + 1)) - 1 and g(x) = (3(2((2(2|x + 3| + 1) + 1)/(-1(2|x + 3| + 1) - 3))^2) - 2)/(2(2((2(2|x + 3| + 1) + 1)/(-1(2|x + 3| + 1) - 3))^2) + 1) from x = 1.4 to x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
15.3
|
math
|
train
|
math_algebra_func_area_level_4_4_448
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 1|(-3(2((1(-2sin(1πx - 1)) - 1)/(3(-2sin(1πx - 1)) - 1)) + 5) - 5) + 3| - 2 and g(x) = 1(4(-5(-4x)^2 + 2(-4x) - 1)^2 - 2(-5(-4x)^2 + 2(-4x) - 1) - 4) + 1 between the vertical lines x = -0.2 and x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.9
|
math
|
train
|
math_algebra_func_area_level_4_4_449
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 3cos(2π(-3|((2(2|((2x)/(-2x - 2)) + 1| - 3) - 1)/(1(2|((2x)/(-2x - 2)) + 1| - 3) - 3)) + 3| + 3) - 1) + 1 and g(x) = 5(1|((-3(-2|x - 2|))/(3(-2|x - 2|) + 1)) - 2| - 3)^2 + 1(1|((-3(-2|x - 2|))/(3(-2|x - 2|) + 1)) - 2| - 3) - 1 from x = -0.4 to x = -0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_4_4_450
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (3(2(-2|(2cos(2π(2|x + 2| + 3) - 2) + 1)| - 1) - 3) - 2)/(-1(2(-2|(2cos(2π(2|x + 2| + 3) - 2) + 1)| - 1) - 3) - 1) and g(x) = 5(-4(-2(1|x - 2| - 2)) - 1) + 5 from x = 0.1 to x = 3.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
145.9
|
math
|
train
|
math_algebra_func_area_level_4_4_451
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -2|(-2|(1((-1(1x^2 - 4x - 2) - 2)/(-1(1x^2 - 4x - 2) - 2))) - 1| - 2) - 3|, g(x) = -2|(2|(-4(-3sin(3πx - 1) - 1)^2 - 5(-3sin(3πx - 1) - 1) + 4) + 1| - 1) - 3| + 2, x = -1.2, and x = -1.0999999999999999. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4.8
|
math
|
train
|
math_algebra_func_area_level_4_4_452
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -2|(-1sin(3π(1(1|(5x - 4) + 3| - 3) + 1) + 3) - 3) + 2| and g(x) = -3e^(-2(3|(4(1|x - 1| + 3) + 5) + 1| - 2)) - 1 between the vertical lines x = -0.3 and x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_4_4_453
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 5(3|(-2|(1(-5x^2 - 4x + 5)^2 + 3(-5x^2 - 4x + 5)) - 3| - 1) + 2| - 3)^2 + 2(3|(-2|(1(-5x^2 - 4x + 5)^2 + 3(-5x^2 - 4x + 5)) - 3| - 1) + 2| - 3) and g(x) = 1cos(3π((1(-3|(2x - 5) - 2| - 3) - 1)/(1(-3|(2x - 5) - 2| - 3))) + 2) between the vertical lines x = -1.4 and x = -1.2999999999999998. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
87.4
|
math
|
train
|
math_algebra_func_area_level_4_4_454
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1(5((1(3(-2|x - 2|) + 5) - 3)/(1(3(-2|x - 2|) + 5) + 1)) - 5) + 3 and g(x) = -3sin(1π(-2(-3((1x + 1)/(-2x + 1)) - 3) - 2) - 1) from x = 1.6 to x = 1.7000000000000002. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.0
|
math
|
train
|
math_algebra_func_area_level_4_4_455
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3cos(1π(-4(-4(1(1x - 4)^2 - 3(1x - 4) + 2) - 1)^2 - 2(-4(1(1x - 4)^2 - 3(1x - 4) + 2) - 1) - 1)) + 2, g(x) = (-1((-2(2(1x - 2) - 1) + 3)/(-3(2(1x - 2) - 1) + 2)) + 2)/(-2((-2(2(1x - 2) - 1) + 3)/(-3(2(1x - 2) - 1) + 2)) - 3), x = 1.3, and x = 1.4000000000000001. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_4_4_456
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (1(5((-1((-2(-3cos(2πx + 2) + 1) + 1)/(2(-3cos(2πx + 2) + 1) + 1)) - 2)/(-1((-2(-3cos(2πx + 2) + 1) + 1)/(2(-3cos(2πx + 2) + 1) + 1)) - 3))) - 2)/(2(5((-1((-2(-3cos(2πx + 2) + 1) + 1)/(2(-3cos(2πx + 2) + 1) + 1)) - 2)/(-1((-2(-3cos(2πx + 2) + 1) + 1)/(2(-3cos(2πx + 2) + 1) + 1)) - 3))) + 3) and g(x) = 1(4(1((3x + 3)/(1x)) + 2)^2 + 4(1((3x + 3)/(1x)) + 2) - 2) - 1 from x = -0.7 to x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.5
|
math
|
train
|
math_algebra_func_area_level_4_4_457
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (-2((-2(2|(2cos(3π(-2x + 3) - 3)) - 3| - 3) + 1)/(-2(2|(2cos(3π(-2x + 3) - 3)) - 3| - 3) - 3)) - 1)/(-3((-2(2|(2cos(3π(-2x + 3) - 3)) - 3| - 3) + 1)/(-2(2|(2cos(3π(-2x + 3) - 3)) - 3| - 3) - 3)) - 3) and g(x) = 1|(-3sin(1π(-1(-5x + 2)^2 + 5) + 3) - 1) - 1| + 3 between the vertical lines x = -0.0 and x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.4
|
math
|
train
|
math_algebra_func_area_level_4_4_458
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -2|(-2(-1|(1(-1x^2 + 2x - 4)^2 - 1(-1x^2 + 2x - 4) - 4) - 3| + 3)^2 - 2(-1|(1(-1x^2 + 2x - 4)^2 - 1(-1x^2 + 2x - 4) - 4) - 3| + 3) - 5)| and g(x) = -2|(3|(-4((-2x + 3)/(-2x - 3)) + 4) + 3| + 2) + 3| + 1 from x = 0.4 to x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
29.1
|
math
|
train
|
math_algebra_func_area_level_4_4_459
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 2sin(3π(3(1|(3|(-1x^2 + 1x - 1) + 1| - 1)|)^2 - 2(1|(3|(-1x^2 + 1x - 1) + 1| - 1)|) - 1) + 3) and g(x) = (-1((3((1(-5x - 1) + 1)/(1(-5x - 1) - 2)) - 1)/(2((1(-5x - 1) + 1)/(1(-5x - 1) - 2)) - 1)))/(-2((3((1(-5x - 1) + 1)/(1(-5x - 1) - 2)) - 1)/(2((1(-5x - 1) + 1)/(1(-5x - 1) - 2)) - 1)) - 3) between the vertical lines x = -2.7 and x = -2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_4_4_460
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -1((-1(-4(-3e^(-1(-4x + 3)) + 2) + 1) - 2)/(2(-4(-3e^(-1(-4x + 3)) + 2) + 1) + 2)) + 3 and g(x) = (3(3|(-1cos(1π(-1|x + 2| - 3)) + 3) - 3| - 3))/(-1(3|(-1cos(1π(-1|x + 2| - 3)) + 3) - 3| - 3) - 3) between the vertical lines x = 1.4 and x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
44.2
|
math
|
train
|
math_algebra_func_area_level_4_4_461
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1|(-3((-3(-4(-2|x - 3| + 3) + 5) + 2)/(-2(-4(-2|x - 3| + 3) + 5) + 3))^2 - 2((-3(-4(-2|x - 3| + 3) + 5) + 2)/(-2(-4(-2|x - 3| + 3) + 5) + 3)) - 4)| and g(x) = 5((2((1((-1x)/(-3x)) - 1)/(-1((-1x)/(-3x)) - 1)) - 1)/(-1((1((-1x)/(-3x)) - 1)/(-1((-1x)/(-3x)) - 1)) + 3))^2 + 3((2((1((-1x)/(-3x)) - 1)/(-1((-1x)/(-3x)) - 1)) - 1)/(-1((1((-1x)/(-3x)) - 1)/(-1((-1x)/(-3x)) - 1)) + 3)) + 4 from x = 2.0 to x = 2.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_4_4_462
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 2((2((2(3|(1x - 2) - 1| - 2) + 2)/(-1(3|(1x - 2) - 1| - 2) + 2)) + 3)/(3((2(3|(1x - 2) - 1| - 2) + 2)/(-1(3|(1x - 2) - 1| - 2) + 2)) + 1)) + 3 and g(x) = (-3(-2e^(1(-1(2|x| + 3)^2 + 4(2|x| + 3) + 2)) + 1) - 1)/(-2(-2e^(1(-1(2|x| + 3)^2 + 4(2|x| + 3) + 2)) + 1) - 1) from x = -0.8 to x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.9
|
math
|
train
|
math_algebra_func_area_level_4_4_463
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1((3(5(1(-5x + 5)^2 - 2(-5x + 5) + 4) + 5))/(-2(5(1(-5x + 5)^2 - 2(-5x + 5) + 4) + 5) + 3)) - 1 and g(x) = -5(-5(2(-1x^2 - 5x) + 2)^2 - 3(2(-1x^2 - 5x) + 2))^2 - 4(-5(2(-1x^2 - 5x) + 2)^2 - 3(2(-1x^2 - 5x) + 2)) from x = 0.2 to x = 0.30000000000000004. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.6
|
math
|
train
|
math_algebra_func_area_level_4_4_464
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -1|(2(-2e^(1((-2(-3x^2 + 4) - 1)/(-3(-3x^2 + 4) - 3))) + 1)^2 + 3(-2e^(1((-2(-3x^2 + 4) - 1)/(-3(-3x^2 + 4) - 3))) + 1) - 5) + 2| - 3, g(x) = -2|(4((3(-2x - 2) + 3)/(2(-2x - 2) - 1))^2 - 5((3(-2x - 2) + 3)/(2(-2x - 2) - 1)) - 3) - 3|, x = -0.8, and x = -0.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_4_4_465
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (-3((3(-3(3|((-3x + 3)/(2x - 1))|) + 5) - 3)/(-1(-3(3|((-3x + 3)/(2x - 1))|) + 5) + 3)))/(-2((3(-3(3|((-3x + 3)/(2x - 1))|) + 5) - 3)/(-1(-3(3|((-3x + 3)/(2x - 1))|) + 5) + 3)) - 1) and g(x) = (2(-2cos(2π(4(1x + 2) + 4) + 3) + 3) + 2)/(-1(-2cos(2π(4(1x + 2) + 4) + 3) + 3) + 2) between the vertical lines x = 0.9 and x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
6.9
|
math
|
train
|
math_algebra_func_area_level_4_4_466
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -4(-3e^(-1(3(-4(2x - 2) + 5)^2 - 5(-4(2x - 2) + 5) - 3)) - 1) - 5 and g(x) = -5(-2(3|(-3x + 4) - 3| - 1)^2 - 2(3|(-3x + 4) - 3| - 1) + 2)^2 - 3(-2(3|(-3x + 4) - 3| - 1)^2 - 2(3|(-3x + 4) - 3| - 1) + 2) + 1 from x = 0.2 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
8.3
|
math
|
train
|
math_algebra_func_area_level_4_4_467
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (1(-4(-3cos(3π((1(-1|x + 3| - 3) - 2)/(-1(-1|x + 3| - 3) - 2)) - 3) - 3)) - 1)/(-1(-4(-3cos(3π((1(-1|x + 3| - 3) - 2)/(-1(-1|x + 3| - 3) - 2)) - 3) - 3))) and g(x) = 1|(-3|(2|(2x^2 - 5x - 5) - 2| + 2) - 2| + 2) - 1| - 2 from x = -3.7 to x = -3.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
82.6
|
math
|
train
|
math_algebra_func_area_level_4_4_468
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -2|((-1((2(1(-2|x - 1|) + 4) - 3)/(-2(1(-2|x - 1|) + 4) + 3)) + 3)/(-3((2(1(-2|x - 1|) + 4) - 3)/(-2(1(-2|x - 1|) + 4) + 3)) - 1)) + 1| + 1 and g(x) = -2|(-3cos(1π(-5(3x - 5)^2 - 1(3x - 5)) - 1) + 2) + 3| + 2 between the vertical lines x = -3.7 and x = -3.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.4
|
math
|
train
|
math_algebra_func_area_level_4_4_469
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -5((1((3(-3(4x - 1)^2 + 1(4x - 1) + 2) + 2)/(-3(-3(4x - 1)^2 + 1(4x - 1) + 2) + 1)) - 3)/(2((3(-3(4x - 1)^2 + 1(4x - 1) + 2) + 2)/(-3(-3(4x - 1)^2 + 1(4x - 1) + 2) + 1)) - 1)) - 4, g(x) = 4(1(1(2|x - 1| + 2) - 3)^2 + 3(1(2|x - 1| + 2) - 3) - 1)^2 + 2(1(1(2|x - 1| + 2) - 3)^2 + 3(1(2|x - 1| + 2) - 3) - 1) - 5, x = 0.1, and x = 0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.4
|
math
|
train
|
math_algebra_func_area_level_4_4_470
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -5((-3(1(3|(-1x - 3) + 3|)^2 + 5(3|(-1x - 3) + 3|) + 3))/(2(1(3|(-1x - 3) + 3|)^2 + 5(3|(-1x - 3) + 3|) + 3) - 3)) + 1 and g(x) = 1(2|(-2|(1cos(2πx - 2) + 2) - 1| + 2) - 3|)^2 + 1(2|(-2|(1cos(2πx - 2) + 2) - 1| + 2) - 3|) - 4 from x = -4.1 to x = -3.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
38.6
|
math
|
train
|
math_algebra_func_area_level_4_4_471
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-3(-1((2(2|(-3|x + 3| + 3) + 3| - 3) + 3)/(3(2|(-3|x + 3| + 3) + 3| - 3)))^2 + 3((2(2|(-3|x + 3| + 3) + 3| - 3) + 3)/(3(2|(-3|x + 3| + 3) + 3| - 3))) - 5))/(1(-1((2(2|(-3|x + 3| + 3) + 3| - 3) + 3)/(3(2|(-3|x + 3| + 3) + 3| - 3)))^2 + 3((2(2|(-3|x + 3| + 3) + 3| - 3) + 3)/(3(2|(-3|x + 3| + 3) + 3| - 3))) - 5) - 2), g(x) = -4((-2(2|(1x^2 - 4x + 3)|))/(2(2|(1x^2 - 4x + 3)|) - 1)) + 4, x = 2.9, and x = 3.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.8
|
math
|
train
|
math_algebra_func_area_level_4_4_472
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (-2(-3(-3(-3e^(2(-1x - 2)) + 3)^2 - 4(-3e^(2(-1x - 2)) + 3)) + 2) + 2)/(-1(-3(-3(-3e^(2(-1x - 2)) + 3)^2 - 4(-3e^(2(-1x - 2)) + 3)) + 2) + 2) and g(x) = (-2(4(-5(2x - 1)^2 + 3(2x - 1) + 5) - 4) + 2)/(3(4(-5(2x - 1)^2 + 3(2x - 1) + 5) - 4) - 2) between the vertical lines x = -2.2 and x = -2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.0
|
math
|
train
|
math_algebra_func_area_level_4_4_473
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 2e^(-1(2((-3(1(-2|x + 2| - 1) + 4) - 1)/(-3(1(-2|x + 2| - 1) + 4)))^2 + 1((-3(1(-2|x + 2| - 1) + 4) - 1)/(-3(1(-2|x + 2| - 1) + 4))) - 4)) + 1 and g(x) = 2(-1(-5(-2x + 1) - 3)^2 + 1(-5(-2x + 1) - 3) + 3)^2 - 2(-1(-5(-2x + 1) - 3)^2 + 1(-5(-2x + 1) - 3) + 3) - 3 between the vertical lines x = 0.6 and x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.9
|
math
|
train
|
math_algebra_func_area_level_4_4_474
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-3(5((2(1sin(2π(3x^2 - 5x + 1) - 3) + 1) + 3)/(-2(1sin(2π(3x^2 - 5x + 1) - 3) + 1) + 3))^2 + 3((2(1sin(2π(3x^2 - 5x + 1) - 3) + 1) + 3)/(-2(1sin(2π(3x^2 - 5x + 1) - 3) + 1) + 3)) + 2) + 3)/(3(5((2(1sin(2π(3x^2 - 5x + 1) - 3) + 1) + 3)/(-2(1sin(2π(3x^2 - 5x + 1) - 3) + 1) + 3))^2 + 3((2(1sin(2π(3x^2 - 5x + 1) - 3) + 1) + 3)/(-2(1sin(2π(3x^2 - 5x + 1) - 3) + 1) + 3)) + 2) + 1), g(x) = 4(1e^(1(1((-3x + 2)/(-3x)))) - 2) - 2, x = 3.5, and x = 3.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.0
|
math
|
train
|
math_algebra_func_area_level_4_4_475
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-1(-1(-4(-3(-2|x + 3| - 1)^2 + 3(-2|x + 3| - 1)))^2 - 4(-4(-3(-2|x + 3| - 1)^2 + 3(-2|x + 3| - 1))) - 2) - 2)/(-1(-1(-4(-3(-2|x + 3| - 1)^2 + 3(-2|x + 3| - 1)))^2 - 4(-4(-3(-2|x + 3| - 1)^2 + 3(-2|x + 3| - 1))) - 2)), g(x) = (1(2|(-1(2sin(2πx - 3) + 2)^2 - 2(2sin(2πx - 3) + 2) + 4) - 2| - 3) + 2)/(-1(2|(-1(2sin(2πx - 3) + 2)^2 - 2(2sin(2πx - 3) + 2) + 4) - 2| - 3) - 3), x = 3.1, and x = 3.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_4_4_476
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-2((-1(-1((-1(-5x^2 - 5x + 2) + 2)/(-3(-5x^2 - 5x + 2) - 1))) - 2)/(3(-1((-1(-5x^2 - 5x + 2) + 2)/(-3(-5x^2 - 5x + 2) - 1))) + 3)))/(-1((-1(-1((-1(-5x^2 - 5x + 2) + 2)/(-3(-5x^2 - 5x + 2) - 1))) - 2)/(3(-1((-1(-5x^2 - 5x + 2) + 2)/(-3(-5x^2 - 5x + 2) - 1))) + 3)) + 3) and g(x) = 3|((-2(-2|((1x)/(3x + 1)) + 3| + 1) + 2)/(-1(-2|((1x)/(3x + 1)) + 3| + 1) - 2)) + 2| + 1 from x = -1.5 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
35.0
|
math
|
train
|
math_algebra_func_area_level_4_4_477
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -4(5(4(-4(1cos(1πx) + 1)^2 + 5(1cos(1πx) + 1) + 2)^2 - 3(-4(1cos(1πx) + 1)^2 + 5(1cos(1πx) + 1) + 2) - 3) - 1) + 5 and g(x) = 1(-5((1((-3x - 3)/(1x - 3)) - 2)/(-1((-3x - 3)/(1x - 3)) + 2))^2 + 4((1((-3x - 3)/(1x - 3)) - 2)/(-1((-3x - 3)/(1x - 3)) + 2)) + 3) - 1 from x = 3.6 to x = 3.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
5.8
|
math
|
train
|
math_algebra_func_area_level_4_4_478
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 1|((-2(-1(-2|(2x + 3) - 2| + 3)^2 + 2(-2|(2x + 3) - 2| + 3) - 4))/(2(-1(-2|(2x + 3) - 2| + 3)^2 + 2(-2|(2x + 3) - 2| + 3) - 4) + 3)) - 1|, g(x) = 2cos(1π(5(2|(2x + 3) + 3| - 2)^2 + 2(2|(2x + 3) + 3| - 2) - 2) - 1) + 3, x = -2.1, and x = -2.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_4_4_479
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -2|(1(3(1|(2sin(1πx - 3) + 1) - 2|)^2 + 5(1|(2sin(1πx - 3) + 1) - 2|))^2 + 5) + 1| - 1 and g(x) = -3|(-3(-3((1x + 3)/(2x)) + 4)^2 + 4(-3((1x + 3)/(2x)) + 4) + 4)| - 2 between the vertical lines x = -3.0 and x = -2.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
17.8
|
math
|
train
|
math_algebra_func_area_level_4_4_480
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -2(-2|(-4((-3(5x - 5) - 1)/(3(5x - 5) - 1))^2 - 2((-3(5x - 5) - 1)/(3(5x - 5) - 1)) + 3)| + 2)^2 + 3(-2|(-4((-3(5x - 5) - 1)/(3(5x - 5) - 1))^2 - 2((-3(5x - 5) - 1)/(3(5x - 5) - 1)) + 3)| + 2) + 1 and g(x) = (-2(2sin(1π(-1|(-3x - 3) - 2| - 1) + 1)) - 3)/(-2(2sin(1π(-1|(-3x - 3) - 2| - 1) + 1)) - 1) from x = -0.9 to x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.1
|
math
|
train
|
math_algebra_func_area_level_4_4_481
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -2(-1((2(-3(-1|x - 1| + 2)^2 - 5(-1|x - 1| + 2) - 1) - 3)/(2(-3(-1|x - 1| + 2)^2 - 5(-1|x - 1| + 2) - 1) - 1))^2 + 3((2(-3(-1|x - 1| + 2)^2 - 5(-1|x - 1| + 2) - 1) - 3)/(2(-3(-1|x - 1| + 2)^2 - 5(-1|x - 1| + 2) - 1) - 1)) - 3) - 5 and g(x) = -1(2(-2cos(3π(-5x + 5) - 2) + 1) + 2)^2 - 1(2(-2cos(3π(-5x + 5) - 2) + 1) + 2) + 5 from x = 2.8 to x = 2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.3
|
math
|
train
|
math_algebra_func_area_level_4_4_482
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 5(2(-1(5(1sin(2πx) + 2)^2 - 1(1sin(2πx) + 2) - 5) + 2)^2 - 3(-1(5(1sin(2πx) + 2)^2 - 1(1sin(2πx) + 2) - 5) + 2) - 1)^2 + 5(2(-1(5(1sin(2πx) + 2)^2 - 1(1sin(2πx) + 2) - 5) + 2)^2 - 3(-1(5(1sin(2πx) + 2)^2 - 1(1sin(2πx) + 2) - 5) + 2) - 1) + 1, g(x) = 3|(2((1((2x + 3)/(-1x - 3)) + 3)/(-3((2x + 3)/(-1x - 3)))) + 5) - 2| + 3, x = -4.2, and x = -4.1000000000000005. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.6
|
math
|
train
|
math_algebra_func_area_level_4_4_483
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1|(1(1|(3(-1e^(-1x) + 1)^2 - 3(-1e^(-1x) + 1) + 4) + 2| - 3) + 5) + 2| - 3 and g(x) = -3|((-2(-3|(1e^(1x) + 3) - 3| + 3) - 1)/(1(-3|(1e^(1x) + 3) - 3| + 3) + 1)) + 3| - 1 from x = 0.2 to x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
32.1
|
math
|
train
|
math_algebra_func_area_level_4_4_484
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 4(3|(1|(4(-2cos(3πx + 2) - 2) + 4)| + 3) + 2|)^2 - 4(3|(1|(4(-2cos(3πx + 2) - 2) + 4)| + 3) + 2|) + 3 and g(x) = 2((2(4((-3x + 3)/(2x + 3)) + 3) - 2)/(1(4((-3x + 3)/(2x + 3)) + 3)))^2 + 4((2(4((-3x + 3)/(2x + 3)) + 3) - 2)/(1(4((-3x + 3)/(2x + 3)) + 3))) - 3 from x = 3.4 to x = 3.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
22.0
|
math
|
train
|
math_algebra_func_area_level_4_4_485
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -5(-3(1|((2(4x + 1) - 3)/(3(4x + 1))) - 2| - 3) - 4) - 5 and g(x) = (-2(2|(4(-1sin(3πx + 1) + 3)^2 + 3) - 3| + 3) + 3)/(-3(2|(4(-1sin(3πx + 1) + 3)^2 + 3) - 3| + 3) - 1) between the vertical lines x = -0.3 and x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
176.2
|
math
|
train
|
math_algebra_func_area_level_4_4_486
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 2(-3|(-3(-2(-1x^2 + 5x - 1)^2 + 3(-1x^2 + 5x - 1) + 2) + 5)| - 1)^2 + 4(-3|(-3(-2(-1x^2 + 5x - 1)^2 + 3(-1x^2 + 5x - 1) + 2) + 5)| - 1) - 2 and g(x) = (2(1((1(3cos(1πx + 1) + 2))/(2(3cos(1πx + 1) + 2) - 1)) - 3) - 1)/(2(1((1(3cos(1πx + 1) + 2))/(2(3cos(1πx + 1) + 2) - 1)) - 3) - 1) from x = 4.4 to x = 4.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4.7
|
math
|
train
|
math_algebra_func_area_level_4_4_487
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3|((-3(-3|(2cos(3π((-2x + 3)/(-2x - 3)) - 3) - 1) - 1| + 2) + 2)/(-2(-3|(2cos(3π((-2x + 3)/(-2x - 3)) - 3) - 1) - 1| + 2))) - 1| + 3, g(x) = 3((3(-1sin(3π(-1x^2 + 1x - 1) - 1) - 3) - 1)/(2(-1sin(3π(-1x^2 + 1x - 1) - 1) - 3) + 3)) - 4, x = -1.8, and x = -1.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_4_4_488
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1|(-3|((2((2(-2|x - 3| - 2) - 1)/(1(-2|x - 3| - 2))))/(1((2(-2|x - 3| - 2) - 1)/(1(-2|x - 3| - 2))) + 2)) - 1| - 1) - 3| - 1 and g(x) = (3(-1sin(1π(3|(-4x^2 - 5x - 3) - 3| + 3) - 1) + 1) - 2)/(-2(-1sin(1π(3|(-4x^2 - 5x - 3) - 3| + 3) - 1) + 1)) from x = 4.0 to x = 4.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
91.7
|
math
|
train
|
math_algebra_func_area_level_4_4_489
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -1(1|(-2(-2(-1|x + 3| + 1)^2 + 4(-1|x + 3| + 1) + 2) - 4) + 2| + 3) + 5 and g(x) = (1(3sin(3π(-2|((2x - 2)/(-3x + 2)) - 1| - 1)) + 3))/(-1(3sin(3π(-2|((2x - 2)/(-3x + 2)) - 1| - 1)) + 3)) between the vertical lines x = -4.8 and x = -4.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.7
|
math
|
train
|
math_algebra_func_area_level_4_4_490
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (1((-1((-1(3cos(3π((-3x)/(2x - 1)) - 1) + 3) + 2)/(1(3cos(3π((-3x)/(2x - 1)) - 1) + 3) - 3)) + 3)/(1((-1(3cos(3π((-3x)/(2x - 1)) - 1) + 3) + 2)/(1(3cos(3π((-3x)/(2x - 1)) - 1) + 3) - 3)) - 2)) - 1)/(-3((-1((-1(3cos(3π((-3x)/(2x - 1)) - 1) + 3) + 2)/(1(3cos(3π((-3x)/(2x - 1)) - 1) + 3) - 3)) + 3)/(1((-1(3cos(3π((-3x)/(2x - 1)) - 1) + 3) + 2)/(1(3cos(3π((-3x)/(2x - 1)) - 1) + 3) - 3)) - 2))) and g(x) = (3(2e^(1(-2|(1x^2 - 3x + 4) - 3| + 2)) - 3))/(3(2e^(1(-2|(1x^2 - 3x + 4) - 3| + 2)) - 3) - 2) between the vertical lines x = 2.9 and x = 3.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.4
|
math
|
train
|
math_algebra_func_area_level_4_4_491
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 1|(-2|(2(5(1x^2 + 3x + 3)^2 + 1(1x^2 + 3x + 3) - 2) - 4)| + 1) - 1| and g(x) = 2e^(-1(-3|((1(-2x^2 + 3x - 3) + 1)/(1(-2x^2 + 3x - 3) + 2)) - 3| - 2)) + 2 between the vertical lines x = 0.0 and x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
52.1
|
math
|
train
|
math_algebra_func_area_level_4_4_492
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -3((-3(-1(-2|(4x^2 + 4x + 5) - 1| + 1)) - 3)/(-1(-1(-2|(4x^2 + 4x + 5) - 1| + 1)) + 2))^2 + 4((-3(-1(-2|(4x^2 + 4x + 5) - 1| + 1)) - 3)/(-1(-1(-2|(4x^2 + 4x + 5) - 1| + 1)) + 2)) - 3 and g(x) = -5(1(2(-3cos(2πx + 2) - 2) + 3) - 4)^2 - 2(1(2(-3cos(2πx + 2) - 2) + 3) - 4) + 1 between the vertical lines x = -2.0 and x = -1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
8.5
|
math
|
train
|
math_algebra_func_area_level_4_4_493
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (3(1(1(-4(-2e^(1x) - 2)^2 - 2(-2e^(1x) - 2) - 3)^2 + 2(-4(-2e^(1x) - 2)^2 - 2(-2e^(1x) - 2) - 3) + 2)^2 - 2(1(-4(-2e^(1x) - 2)^2 - 2(-2e^(1x) - 2) - 3)^2 + 2(-4(-2e^(1x) - 2)^2 - 2(-2e^(1x) - 2) - 3) + 2) + 3) - 2)/(3(1(1(-4(-2e^(1x) - 2)^2 - 2(-2e^(1x) - 2) - 3)^2 + 2(-4(-2e^(1x) - 2)^2 - 2(-2e^(1x) - 2) - 3) + 2)^2 - 2(1(-4(-2e^(1x) - 2)^2 - 2(-2e^(1x) - 2) - 3)^2 + 2(-4(-2e^(1x) - 2)^2 - 2(-2e^(1x) - 2) - 3) + 2) + 3) - 2), g(x) = -1e^(1(4(-5((1x - 1)/(2x - 1))^2 + 4((1x - 1)/(2x - 1)) + 2) + 2)) + 1, x = 0.3, and x = 0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.0
|
math
|
train
|
math_algebra_func_area_level_4_4_494
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1cos(3π(-2|(5(-5((-2x - 2)/(1x + 2))^2 - 4((-2x - 2)/(1x + 2)) - 2)^2 + 2(-5((-2x - 2)/(1x + 2))^2 - 4((-2x - 2)/(1x + 2)) - 2) - 5) + 3| + 3) + 1) + 3 and g(x) = 1(3e^(-1(1(-1x^2 + 1x + 4) - 4)) + 3) - 5 from x = 1.3 to x = 1.4000000000000001. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_4_4_495
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -5(-2cos(1π((-1((2(-1|x + 3| + 2) + 1)/(1(-1|x + 3| + 2) - 3)) + 2)/(2((2(-1|x + 3| + 2) + 1)/(1(-1|x + 3| + 2) - 3)) - 1)) - 2) - 1) - 4 and g(x) = (-2(4(-1|(-1|x + 3| - 3) - 3| + 3) - 1))/(-2(4(-1|(-1|x + 3| - 3) - 3| + 3) - 1) - 3) from x = 1.1 to x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.7
|
math
|
train
|
math_algebra_func_area_level_4_4_496
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (-1(2(4(4(-3|x + 2| + 2)^2 - 5(-3|x + 2| + 2) + 1)^2 - 1) - 2))/(-1(2(4(4(-3|x + 2| + 2)^2 - 5(-3|x + 2| + 2) + 1)^2 - 1) - 2) - 2) and g(x) = -1(1|(-5((-2x)/(2x - 3))^2 + 4((-2x)/(2x - 3)) - 5) - 1| - 2) between the vertical lines x = -2.6 and x = -2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.0
|
math
|
train
|
math_algebra_func_area_level_4_4_497
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -4(-5(-1((-2(3x^2 + 1) - 1)/(-3(3x^2 + 1) + 1))) + 5) + 5 and g(x) = -1|((-3((1(1x^2 - 5x + 4) - 2)/(1(1x^2 - 5x + 4))) - 3)/(-2((1(1x^2 - 5x + 4) - 2)/(1(1x^2 - 5x + 4))) + 1)) - 2| - 1 from x = -0.1 to x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
148.5
|
math
|
train
|
math_algebra_func_area_level_4_4_498
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -4(1|((3(-3(-2e^(-2x) - 2)^2 + 5(-2e^(-2x) - 2) + 3))/(-1(-3(-2e^(-2x) - 2)^2 + 5(-2e^(-2x) - 2) + 3) + 3)) + 3| + 1)^2 + 4(1|((3(-3(-2e^(-2x) - 2)^2 + 5(-2e^(-2x) - 2) + 3))/(-1(-3(-2e^(-2x) - 2)^2 + 5(-2e^(-2x) - 2) + 3) + 3)) + 3| + 1) + 3, g(x) = 2|(2|(3cos(2π(4x - 5) - 2) - 3) + 2| - 3) - 2| + 1, x = -3.6, and x = -3.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_4_4_499
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -4(-1(1(-1(3cos(1πx + 2) - 1)^2 - 4(3cos(1πx + 2) - 1) - 1) + 1)^2 + 2(1(-1(3cos(1πx + 2) - 1)^2 - 4(3cos(1πx + 2) - 1) - 1) + 1) - 2)^2 + 5(-1(1(-1(3cos(1πx + 2) - 1)^2 - 4(3cos(1πx + 2) - 1) - 1) + 1)^2 + 2(1(-1(3cos(1πx + 2) - 1)^2 - 4(3cos(1πx + 2) - 1) - 1) + 1) - 2) - 4, g(x) = -2(4(3((2x - 2)/(-2x - 3))^2 + 5((2x - 2)/(-2x - 3)) + 3) - 1) + 3, x = -3.4, and x = -3.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
61.7
|
math
|
train
|
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