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_100
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 2(-2sin(2π(-1(-5(2|x - 1| - 3)^2 - 4(2|x - 1| - 3) + 3) - 2) + 3) + 1)^2 - 3(-2sin(2π(-1(-5(2|x - 1| - 3)^2 - 4(2|x - 1| - 3) + 3) - 2) + 3) + 1) - 1, g(x) = (1(-5(5(-5x^2 + 3x - 1)^2 + 3(-5x^2 + 3x - 1) - 4)^2 - 5(5(-5x^2 + 3x - 1)^2 + 3(-5x^2 + 3x - 1) - 4) - 4) - 1)/(-3(-5(5(-5x^2 + 3x - 1)^2 + 3(-5x^2 + 3x - 1) - 4)^2 - 5(5(-5x^2 + 3x - 1)^2 + 3(-5x^2 + 3x - 1) - 4) - 4) + 1), x = -0.0, and x = 0.1. Round your answer 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_101
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 1cos(2π(-1|(-3(-3|((1x)/(-2x - 3)) + 1| - 1) - 1) - 3| + 3) - 2) - 2, g(x) = -1|(-3sin(3π(-1|(1x^2 - 5x + 1) + 3| + 2) + 1) - 3) + 3| - 2, x = -1.5, and x = -1.4. 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_102
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -1e^(-1(3|(2(4(3x^2 - 3x - 5) + 1) + 4) - 3| - 3)) - 2 and g(x) = 3((3(5(2|x + 2| - 2)^2 + 5(2|x + 2| - 2) - 3) + 2)/(-2(5(2|x + 2| - 2)^2 + 5(2|x + 2| - 2) - 3) + 1)) + 4 between the vertical lines x = -1.9 and x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
13.0
|
math
|
train
|
math_algebra_func_area_level_4_4_103
|
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(-3|((-1x + 1)/(3x)) - 2| + 3))/(-2(-3|((-1x + 1)/(3x)) - 2| + 3) - 2)) - 1| - 3)^2 + 4(1|((2(-3|((-1x + 1)/(3x)) - 2| + 3))/(-2(-3|((-1x + 1)/(3x)) - 2| + 3) - 2)) - 1| - 3) + 5, g(x) = 4((-1((-2(-1x^2 + 3x - 4))/(-1(-1x^2 + 3x - 4) - 2)) - 2)/(-3((-2(-1x^2 + 3x - 4))/(-1(-1x^2 + 3x - 4) - 2)) - 1))^2, x = 0.1, and x = 0.2. Round your answer 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_104
|
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|((-2(-3(3e^(1x) + 2)^2 - 4(3e^(1x) + 2) + 4) - 1)/(3(-3(3e^(1x) + 2)^2 - 4(3e^(1x) + 2) + 4) - 1)) - 3| + 1) - 3, g(x) = 5(5(1|(-1x^2 + 5x + 1)| - 1)^2 - 5(1|(-1x^2 + 5x + 1)| - 1) + 4)^2 - 5(5(1|(-1x^2 + 5x + 1)| - 1)^2 - 5(1|(-1x^2 + 5x + 1)| - 1) + 4) - 2, x = 4.8, and x = 5.0. Round your answer 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_105
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1|(-5(-1|(-3cos(2π(1|x - 3|) + 3)) + 3| - 2) + 5) + 1| + 2 and g(x) = (-2(1sin(1π(-1(1x - 4)^2 + 2(1x - 4) + 1) + 2) - 1) + 3)/(-3(1sin(1π(-1(1x - 4)^2 + 2(1x - 4) + 1) + 2) - 1) - 3) from x = 0.4 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4.9
|
math
|
train
|
math_algebra_func_area_level_4_4_106
|
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(1e^(-1((-2x - 1)/(-2x - 3))) + 3) + 2)/(2(1e^(-1((-2x - 1)/(-2x - 3))) + 3))) - 1) + 1)/(-1(-4((2(1e^(-1((-2x - 1)/(-2x - 3))) + 3) + 2)/(2(1e^(-1((-2x - 1)/(-2x - 3))) + 3))) - 1) - 2) and g(x) = -1((-2(-3(5x^2 - 2x - 1)^2 + 1(5x^2 - 2x - 1) + 3) - 1)/(-1(-3(5x^2 - 2x - 1)^2 + 1(5x^2 - 2x - 1) + 3) - 3))^2 + 4((-2(-3(5x^2 - 2x - 1)^2 + 1(5x^2 - 2x - 1) + 3) - 1)/(-1(-3(5x^2 - 2x - 1)^2 + 1(5x^2 - 2x - 1) + 3) - 3)) + 5 between the vertical lines x = 0.4 and x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.8
|
math
|
train
|
math_algebra_func_area_level_4_4_107
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-2(-3cos(3π(2|(1((2x - 1)/(1x + 2))^2 + 1)|) - 3) + 3) + 3)/(-2(-3cos(3π(2|(1((2x - 1)/(1x + 2))^2 + 1)|) - 3) + 3) + 1) and g(x) = 2|(1(-1|((-2x + 1)/(1x + 1)) + 3| + 3)^2 - 3(-1|((-2x + 1)/(1x + 1)) + 3| + 3) + 1) + 3| from x = -2.3 to x = -2.2. 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_108
|
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(2e^(-1(1|(-2|x + 1|) + 2| - 2))) + 1)/(3(2e^(-1(1|(-2|x + 1|) + 2| - 2))) + 3)) - 3)/(1((3(2e^(-1(1|(-2|x + 1|) + 2| - 2))) + 1)/(3(2e^(-1(1|(-2|x + 1|) + 2| - 2))) + 3)) - 3) and g(x) = -2sin(1π(2|((-2((-1x + 3)/(-2x - 1)) + 2)/(2((-1x + 3)/(-2x - 1)) + 2)) - 1|) + 1) + 3 between the vertical lines x = 1.0 and x = 1.1. 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_109
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -2|((-1((-3(5(1|x| - 1) - 5) - 1)/(1(5(1|x| - 1) - 5) - 2)) + 3)/(-3((-3(5(1|x| - 1) - 5) - 1)/(1(5(1|x| - 1) - 5) - 2)) - 2)) - 1| + 3, g(x) = (2(1(-5((-3x + 3)/(1x + 1))^2 - 4) + 4) + 1)/(-3(1(-5((-3x + 3)/(1x + 1))^2 - 4) + 4) + 1), x = -1.6, and x = 1.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
9.1
|
math
|
train
|
math_algebra_func_area_level_4_4_110
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-1(-1(-1(1|(-4x - 1) + 2|) + 2)^2 + 3) + 3)/(2(-1(-1(1|(-4x - 1) + 2|) + 2)^2 + 3) - 1) and g(x) = (-2(-1(1(-5x)^2 + 4(-5x) + 2) - 4) - 2)/(3(-1(1(-5x)^2 + 4(-5x) + 2) - 4) + 1) from x = -1.1 to x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
5.2
|
math
|
train
|
math_algebra_func_area_level_4_4_111
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3|(2e^(2((-2(-1((-3x + 1)/(3x - 1)) + 4) + 3)/(-3(-1((-3x + 1)/(3x - 1)) + 4) - 1))))| + 3, g(x) = 2|(3(4(3sin(3πx)) + 4)^2 - 1(4(3sin(3πx)) + 4) - 3) - 2| - 2, x = -3.6, and x = -3.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
23.5
|
math
|
train
|
math_algebra_func_area_level_4_4_112
|
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|(-2cos(2π((3(3|((3x - 1)/(1x + 2)) - 2| + 1) + 1)/(2(3|((3x - 1)/(1x + 2)) - 2| + 1) - 1)) + 3) + 1) - 2| + 2 and g(x) = -3cos(3π((2(4(4x + 3)^2 + 5(4x + 3) + 3))/(1(4(4x + 3)^2 + 5(4x + 3) + 3) + 2)) + 3) - 3 between the vertical lines x = 4.5 and x = 4.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.6
|
math
|
train
|
math_algebra_func_area_level_4_4_113
|
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(-1((-2x - 1)/(-2x + 3))^2 + 2((-2x - 1)/(-2x + 3))) - 3)/(2(-1((-2x - 1)/(-2x + 3))^2 + 2((-2x - 1)/(-2x + 3))) - 1)) + 1| - 3) + 1)/(1(2|((2(-1((-2x - 1)/(-2x + 3))^2 + 2((-2x - 1)/(-2x + 3))) - 3)/(2(-1((-2x - 1)/(-2x + 3))^2 + 2((-2x - 1)/(-2x + 3))) - 1)) + 1| - 3) - 3) and g(x) = 2|((1(-2(2x + 1)^2 + 4(2x + 1) - 3) - 2)/(3(-2(2x + 1)^2 + 4(2x + 1) - 3))) - 1| + 2 between the vertical lines x = -2.2 and x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
14.0
|
math
|
train
|
math_algebra_func_area_level_4_4_114
|
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(-3sin(2π((-2(-4(-5x^2 - 3x + 3) - 3))/(3(-4(-5x^2 - 3x + 3) - 3) - 2))) - 2) + 3)/(1(-3sin(2π((-2(-4(-5x^2 - 3x + 3) - 3))/(3(-4(-5x^2 - 3x + 3) - 3) - 2))) - 2)) and g(x) = 3(-1(1e^(1(-1x - 4)) + 1)^2 - 3(1e^(1(-1x - 4)) + 1) - 1) + 5 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}"
]
}
|
1.9
|
math
|
train
|
math_algebra_func_area_level_4_4_115
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1(3|(5(1((-2x + 1)/(1x - 2))) + 5) + 1| - 2) - 4 and g(x) = (1(1|((2(-3cos(1πx + 1) + 2) - 2)/(-1(-3cos(1πx + 1) + 2))) + 1| - 1))/(2(1|((2(-3cos(1πx + 1) + 2) - 2)/(-1(-3cos(1πx + 1) + 2))) + 1| - 1) + 1) from x = -3.9 to x = -3.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4.3
|
math
|
train
|
math_algebra_func_area_level_4_4_116
|
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(1|(4((-2x + 1)/(-2x - 1))^2 + 3((-2x + 1)/(-2x - 1)) - 2) - 3| - 2)^2 + 5(1|(4((-2x + 1)/(-2x - 1))^2 + 3((-2x + 1)/(-2x - 1)) - 2) - 3| - 2))^2 - 4(-3(1|(4((-2x + 1)/(-2x - 1))^2 + 3((-2x + 1)/(-2x - 1)) - 2) - 3| - 2)^2 + 5(1|(4((-2x + 1)/(-2x - 1))^2 + 3((-2x + 1)/(-2x - 1)) - 2) - 3| - 2)) - 1, g(x) = (3(-3|(-2cos(1π(-2|x - 2| - 2) - 1) - 1) + 2| - 2) - 2)/(-2(-3|(-2cos(1π(-2|x - 2| - 2) - 1) - 1) + 2| - 2) + 3), x = -0.1, and x = 0.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
7.8
|
math
|
train
|
math_algebra_func_area_level_4_4_117
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3|(2|(-2(5(-3|x| + 1) + 1)^2 + 2(5(-3|x| + 1) + 1) + 5) - 2| - 2) + 3|, g(x) = 2|(-2|(1(-1cos(3πx + 2) + 3) + 4) + 1|) - 2| + 1, x = -0.5, and x = -0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
5.7
|
math
|
train
|
math_algebra_func_area_level_4_4_118
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-3(-2(2(-3sin(3π((1x + 1)/(3x)) - 2) - 2)^2 - 2(-3sin(3π((1x + 1)/(3x)) - 2) - 2) - 5)^2 - 1(2(-3sin(3π((1x + 1)/(3x)) - 2) - 2)^2 - 2(-3sin(3π((1x + 1)/(3x)) - 2) - 2) - 5) + 1) - 1)/(-1(-2(2(-3sin(3π((1x + 1)/(3x)) - 2) - 2)^2 - 2(-3sin(3π((1x + 1)/(3x)) - 2) - 2) - 5)^2 - 1(2(-3sin(3π((1x + 1)/(3x)) - 2) - 2)^2 - 2(-3sin(3π((1x + 1)/(3x)) - 2) - 2) - 5) + 1)), g(x) = (3(3(-3(-3cos(2πx) - 2)^2 + 1(-3cos(2πx) - 2) + 5)^2 - 4(-3(-3cos(2πx) - 2)^2 + 1(-3cos(2πx) - 2) + 5) + 2) - 3)/(-1(3(-3(-3cos(2πx) - 2)^2 + 1(-3cos(2πx) - 2) + 5)^2 - 4(-3(-3cos(2πx) - 2)^2 + 1(-3cos(2πx) - 2) + 5) + 2) + 2), x = 2.3, and x = 2.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.5
|
math
|
train
|
math_algebra_func_area_level_4_4_119
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 1sin(1π(-3|((-2(2|(-2x^2 + 3x + 4) - 3|))/(-1(2|(-2x^2 + 3x + 4) - 3|) - 3)) - 3|) + 1) + 2 and g(x) = (-2((-1(-5((2x - 1)/(3x + 3)) + 3) - 2)/(-1(-5((2x - 1)/(3x + 3)) + 3) - 1)))/(-1((-1(-5((2x - 1)/(3x + 3)) + 3) - 2)/(-1(-5((2x - 1)/(3x + 3)) + 3) - 1)) - 1) between the vertical lines x = -0.9 and x = -0.5. 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_120
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-3(4(-2e^(1(1(-2|x + 3| + 3) + 5)))^2 + 5(-2e^(1(1(-2|x + 3| + 3) + 5)))) - 2)/(-2(4(-2e^(1(1(-2|x + 3| + 3) + 5)))^2 + 5(-2e^(1(1(-2|x + 3| + 3) + 5)))) - 3) and g(x) = 1|(1(2((2x + 2)/(1x + 3)) + 4) + 5) + 1| + 1 from x = -2.4 to x = -2.3. 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_121
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-1(-2cos(1π(2|(1(-5x) + 3) - 2|) - 2) + 3) + 3)/(3(-2cos(1π(2|(1(-5x) + 3) - 2|) - 2) + 3) + 1) and g(x) = -4(-3|((3(2e^(-1x) - 2))/(-2(2e^(-1x) - 2) - 1)) + 1| + 2) + 2 from x = -3.8 to x = -3.7. 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_122
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 3e^(1((-2(-1|((-1((1x + 1)/(3x + 2)) + 1)/(1((1x + 1)/(3x + 2)) + 3)) - 2| - 3) + 3)/(3(-1|((-1((1x + 1)/(3x + 2)) + 1)/(1((1x + 1)/(3x + 2)) + 3)) - 2| - 3) - 2))) + 3 and g(x) = -3(-1((-2((-1x)/(-1x - 1)) + 2)/(2((-1x)/(-1x - 1)) - 1))^2 + 4((-2((-1x)/(-1x - 1)) + 2)/(2((-1x)/(-1x - 1)) - 1)) - 5)^2 - 4(-1((-2((-1x)/(-1x - 1)) + 2)/(2((-1x)/(-1x - 1)) - 1))^2 + 4((-2((-1x)/(-1x - 1)) + 2)/(2((-1x)/(-1x - 1)) - 1)) - 5) + 5 from x = 1.7 to x = 2.5. 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_123
|
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(5(-3(-1x^2 - 4x + 5) + 5)^2 + 4(-3(-1x^2 - 4x + 5) + 5) - 2) + 3)/(2(5(-3(-1x^2 - 4x + 5) + 5)^2 + 4(-3(-1x^2 - 4x + 5) + 5) - 2) - 1)) - 1| and g(x) = -1cos(1π(-1|(1(1x + 3)^2 + 2(1x + 3) + 2) + 2| + 2) - 3) - 1 between the vertical lines x = -3 and x = 3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
9.8
|
math
|
train
|
math_algebra_func_area_level_4_4_124
|
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((1(-1(3|(-2|x - 2| - 3) - 3| - 1)^2 - 1(3|(-2|x - 2| - 3) - 3| - 1) + 5) - 1)/(1(-1(3|(-2|x - 2| - 3) - 3| - 1)^2 - 1(3|(-2|x - 2| - 3) - 3| - 1) + 5))) - 3)/(-3((1(-1(3|(-2|x - 2| - 3) - 3| - 1)^2 - 1(3|(-2|x - 2| - 3) - 3| - 1) + 5) - 1)/(1(-1(3|(-2|x - 2| - 3) - 3| - 1)^2 - 1(3|(-2|x - 2| - 3) - 3| - 1) + 5))) + 2) and g(x) = 3(-1(1(-2x + 4) + 5)^2 - 4(1(-2x + 4) + 5) + 2)^2 + 4(-1(1(-2x + 4) + 5)^2 - 4(1(-2x + 4) + 5) + 2) + 4 between the vertical lines x = 4.1 and x = 4.3. 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_125
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1|(2(3|((-1(3|x - 2| - 1) - 2)/(-1(3|x - 2| - 1))) + 3| - 1) + 5) - 3| + 3 and g(x) = 4(-4(-3(3sin(2πx + 3) + 3) + 2)^2)^2 + 3(-4(-3(3sin(2πx + 3) + 3) + 2)^2) - 2 from x = 2.2 to x = 2.3000000000000003. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
68.3
|
math
|
train
|
math_algebra_func_area_level_4_4_126
|
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|(-2sin(3π(1x^2 + 1x - 3) + 3) + 3) - 1| + 1) - 1)/(-2(-1|(-2sin(3π(1x^2 + 1x - 3) + 3) + 3) - 1| + 1)))^2 - 2((-3(-1|(-2sin(3π(1x^2 + 1x - 3) + 3) + 3) - 1| + 1) - 1)/(-2(-1|(-2sin(3π(1x^2 + 1x - 3) + 3) + 3) - 1| + 1))) + 3 and g(x) = (3(-3e^(-1((-2((-2x + 3)/(2x - 1)) - 2)/(-1((-2x + 3)/(2x - 1)) - 2))) - 3) + 1)/(2(-3e^(-1((-2((-2x + 3)/(2x - 1)) - 2)/(-1((-2x + 3)/(2x - 1)) - 2))) - 3)) between the vertical lines x = 4.2 and x = 4.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
233.2
|
math
|
train
|
math_algebra_func_area_level_4_4_127
|
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((-1(2cos(2πx + 2) + 3) + 3)/(3(2cos(2πx + 2) + 3) - 1)) - 1)/(-2((-1(2cos(2πx + 2) + 3) + 3)/(3(2cos(2πx + 2) + 3) - 1)) - 1)) + 1| - 3)^2 - 2, g(x) = (1((1(-1(-3sin(3πx - 2) + 2)^2 + 2(-3sin(3πx - 2) + 2) - 1) + 3)/(-3(-1(-3sin(3πx - 2) + 2)^2 + 2(-3sin(3πx - 2) + 2) - 1))))/(2((1(-1(-3sin(3πx - 2) + 2)^2 + 2(-3sin(3πx - 2) + 2) - 1) + 3)/(-3(-1(-3sin(3πx - 2) + 2)^2 + 2(-3sin(3πx - 2) + 2) - 1))) - 3), x = -2.1, and x = -1.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
5.7
|
math
|
train
|
math_algebra_func_area_level_4_4_128
|
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|(-1|((2(-3x - 4) - 1)/(-3(-3x - 4) + 2)) - 1| - 1) + 3| + 2) + 2, g(x) = (3(-2(5((2x)/(-1x + 2))^2 - 1((2x)/(-1x + 2))) + 4) + 1)/(-1(-2(5((2x)/(-1x + 2))^2 - 1((2x)/(-1x + 2))) + 4) + 3), x = -0.4, and x = 0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
43.9
|
math
|
train
|
math_algebra_func_area_level_4_4_129
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -3(-3(1sin(1π(-2|(-1x + 5) - 1| - 1)) + 2) + 3)^2 + 2(-3(1sin(1π(-2|(-1x + 5) - 1| - 1)) + 2) + 3) - 5 and g(x) = -1e^(2(-3(-2|(-4x^2 + 5) - 1| + 1) - 4)) - 2 from x = 0.8 to x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
28.5
|
math
|
train
|
math_algebra_func_area_level_4_4_130
|
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((-2(2(2|x| - 3) - 5) - 1)/(1(2(2|x| - 3) - 5)))^2 + 1((-2(2(2|x| - 3) - 5) - 1)/(1(2(2|x| - 3) - 5))) - 1) - 1 and g(x) = -3e^(1(-1(3(-1x^2 + 4x + 4)^2 - 3(-1x^2 + 4x + 4) + 5)^2 + 3(3(-1x^2 + 4x + 4)^2 - 3(-1x^2 + 4x + 4) + 5) - 5)) - 2 between the vertical lines x = -2.6 and x = 2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
103.1
|
math
|
train
|
math_algebra_func_area_level_4_4_131
|
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((2((-2(-4(2e^(-2x) - 2)^2 + 2(2e^(-2x) - 2) - 3) + 2)/(-1(-4(2e^(-2x) - 2)^2 + 2(2e^(-2x) - 2) - 3) - 3)) - 2)/(-1((-2(-4(2e^(-2x) - 2)^2 + 2(2e^(-2x) - 2) - 3) + 2)/(-1(-4(2e^(-2x) - 2)^2 + 2(2e^(-2x) - 2) - 3) - 3)) + 2)) + 4 and g(x) = (-2(3sin(1π(-1((-1x - 3)/(-2x + 3)) + 1) - 1) + 3) - 2)/(-2(3sin(1π(-1((-1x - 3)/(-2x + 3)) + 1) - 1) + 3) + 1) between the vertical lines x = 0.9 and x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
5.5
|
math
|
train
|
math_algebra_func_area_level_4_4_132
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-2(1|(1(-4((-1x + 3)/(1x)) - 4)^2 - 2(-4((-1x + 3)/(1x)) - 4) - 4) - 3|) - 2)/(1(1|(1(-4((-1x + 3)/(1x)) - 4)^2 - 2(-4((-1x + 3)/(1x)) - 4) - 4) - 3|) - 3), g(x) = (1(-4(-1|(-2|x + 3| + 3) + 3| + 3)^2 - 2(-1|(-2|x + 3| + 3) + 3| + 3) + 1) - 1)/(-1(-4(-1|(-2|x + 3| + 3) + 3| + 3)^2 - 2(-1|(-2|x + 3| + 3) + 3| + 3) + 1)), x = 1.3, and x = 2.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
5.4
|
math
|
train
|
math_algebra_func_area_level_4_4_133
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -1|(-3sin(2π(2(-1(-2|x + 1| + 3)^2 - 3(-2|x + 1| + 3))^2 - 2(-1(-2|x + 1| + 3)^2 - 3(-2|x + 1| + 3)) + 5)) - 2) - 1| - 3, g(x) = -3(-1(-2|(-3sin(2πx - 3) + 3) - 1| + 1)^2 + 3(-2|(-3sin(2πx - 3) + 3) - 1| + 1) - 3)^2 + 3(-1(-2|(-3sin(2πx - 3) + 3) - 1| + 1)^2 + 3(-2|(-3sin(2πx - 3) + 3) - 1| + 1) - 3), x = -4.4, and x = -4.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
21.3
|
math
|
train
|
math_algebra_func_area_level_4_4_134
|
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(-3cos(3π(-2|(-2|((2x - 1)/(-1x - 3)) + 3| + 2) + 3|) - 3) + 3)^2 + 4(-3cos(3π(-2|(-2|((2x - 1)/(-1x - 3)) + 3| + 2) + 3|) - 3) + 3) - 4 and g(x) = 2e^(-1(-1(1|((-3x + 2)/(3x)) - 2|)^2 + 5(1|((-3x + 2)/(3x)) - 2|) + 4)) + 2 between the vertical lines x = -1.2 and x = -1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.2
|
math
|
train
|
math_algebra_func_area_level_4_4_135
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-1(1((-1(-2(2x^2 + 3x) - 3) + 2)/(2(-2(2x^2 + 3x) - 3) - 1))^2 - 1((-1(-2(2x^2 + 3x) - 3) + 2)/(2(-2(2x^2 + 3x) - 3) - 1)) - 3) + 2)/(-3(1((-1(-2(2x^2 + 3x) - 3) + 2)/(2(-2(2x^2 + 3x) - 3) - 1))^2 - 1((-1(-2(2x^2 + 3x) - 3) + 2)/(2(-2(2x^2 + 3x) - 3) - 1)) - 3)) and g(x) = (2(2|(2|((-1x)/(-2x + 3)) + 1| - 2)|))/(2(2|(2|((-1x)/(-2x + 3)) + 1| - 2)|)) from x = -1.0 to x = -0.5. 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_136
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 1(4(-1|(4(-5x^2 - 2x + 1)^2 + 5(-5x^2 - 2x + 1) - 3) - 2| + 2)^2 - 3(-1|(4(-5x^2 - 2x + 1)^2 + 5(-5x^2 - 2x + 1) - 3) - 2| + 2) + 5) + 4, g(x) = 5(1|(1|(-2sin(3πx - 2) + 3) - 1| + 3) - 1| + 2)^2 - 5(1|(1|(-2sin(3πx - 2) + 3) - 1| + 3) - 1| + 2) + 5, x = -1.0, and x = -0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
81.3
|
math
|
train
|
math_algebra_func_area_level_4_4_137
|
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((-1(2sin(1π(3|(4x^2 - 2x - 4) + 3| - 3) + 2) + 3) + 3)/(1(2sin(1π(3|(4x^2 - 2x - 4) + 3| - 3) + 2) + 3) - 3)) + 4 and g(x) = -4((-3(-2|((1x - 3)/(-3x + 2)) + 2| + 2) - 2)/(-3(-2|((1x - 3)/(-3x + 2)) + 2| + 2) + 2)) - 5 between the vertical lines x = -0.3 and x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
45.9
|
math
|
train
|
math_algebra_func_area_level_4_4_138
|
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((-2x + 3)/(-2x + 1)) + 1) + 2)/(2(1((-2x + 3)/(-2x + 1)) + 1))) - 1| + 3)| - 3 and g(x) = (2(2(-2(1|x + 3| - 2) + 4)^2 - 5(-2(1|x + 3| - 2) + 4)) - 3)/(1(2(-2(1|x + 3| - 2) + 4)^2 - 5(-2(1|x + 3| - 2) + 4))) between the vertical lines x = -3 and x = 3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
53.7
|
math
|
train
|
math_algebra_func_area_level_4_4_139
|
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((-1(-1cos(3π(5x^2 + 4x - 1) - 1) + 1) + 3)/(-2(-1cos(3π(5x^2 + 4x - 1) - 1) + 1) + 3)) - 1) and g(x) = -2((-3((2(2x - 5) - 2)/(-2(2x - 5) - 3)))/(3((2(2x - 5) - 2)/(-2(2x - 5) - 3)) - 2)) - 2 between the vertical lines x = 2.7 and x = 2.8000000000000003. Round 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_140
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -1e^(1((2(-3|(4(-1x^2 + 2x + 1)^2 - 3(-1x^2 + 2x + 1) - 4) + 1| - 2) - 2)/(1(-3|(4(-1x^2 + 2x + 1)^2 - 3(-1x^2 + 2x + 1) - 4) + 1| - 2) - 3))) + 2, g(x) = 3cos(1π((-3(2(-3x - 1) - 2) + 2)/(2(2(-3x - 1) - 2) + 2))) - 2, x = -0.7, and x = -0.6. 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_141
|
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(1|(4(-3|(2|x| + 3) - 2| - 3) + 1) - 2|) + 2) + 3, g(x) = 2|(1cos(3π((-1(2|x - 1| - 2) + 2)/(-1(2|x - 1| - 2) + 2)) - 2) - 1) - 2| - 1, x = -0.7, and x = -0.6. 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_142
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-1(4(1|(2(-3x + 5)^2 + 5(-3x + 5) + 3)| - 3)^2 - 1(1|(2(-3x + 5)^2 + 5(-3x + 5) + 3)| - 3) - 3) - 1)/(2(4(1|(2(-3x + 5)^2 + 5(-3x + 5) + 3)| - 3)^2 - 1(1|(2(-3x + 5)^2 + 5(-3x + 5) + 3)| - 3) - 3)), g(x) = 3|(3(-3(3x + 5)^2 + 4(3x + 5)) + 5) - 2| - 2, x = -1.2, and x = -1.1. 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_143
|
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(2((3x + 1)/(3x - 2))^2 - 3((3x + 1)/(3x - 2)) - 4) - 2)^2 - 1(-1(2((3x + 1)/(3x - 2))^2 - 3((3x + 1)/(3x - 2)) - 4) - 2) - 2) + 5, g(x) = -3sin(2π(-4(5((-1x - 3)/(-2x - 2)) - 4)^2 - 1(5((-1x - 3)/(-2x - 2)) - 4) + 2) - 1) + 2, x = -0.2, and x = -0.1. 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_144
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -5((1(5(4(-1|x| + 1) + 2) + 4) - 3)/(2(5(4(-1|x| + 1) + 2) + 4))) + 2 and g(x) = (-2((3(1(2|x| + 3) + 3) - 3)/(1(1(2|x| + 3) + 3) + 2)))/(-3((3(1(2|x| + 3) + 3) - 3)/(1(1(2|x| + 3) + 3) + 2))) from x = -1.4 to x = 1.4. 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_145
|
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(5(2|x - 3| + 2) - 4)^2 + 1(5(2|x - 3| + 2) - 4)) + 4) - 1)/(-1(-2(2(5(2|x - 3| + 2) - 4)^2 + 1(5(2|x - 3| + 2) - 4)) + 4) + 2) and g(x) = (-2(-5(-3(-4x^2 - 5x + 5)^2 + 4(-4x^2 - 5x + 5) + 5) + 3) + 1)/(-2(-5(-3(-4x^2 - 5x + 5)^2 + 4(-4x^2 - 5x + 5) + 5) + 3)) between the vertical lines x = -1.7 and x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.4
|
math
|
train
|
math_algebra_func_area_level_4_4_146
|
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((-2(2|x - 1|))/(-1(2|x - 1|) + 3)) - 5)^2 + 4(-3((-2(2|x - 1|))/(-1(2|x - 1|) + 3)) - 5)) - 4 and g(x) = -3((-2(2|(-2sin(1πx) + 3) - 3| + 2) + 3)/(-2(2|(-2sin(1πx) + 3) - 3| + 2) - 1))^2 - 2((-2(2|(-2sin(1πx) + 3) - 3| + 2) + 3)/(-2(2|(-2sin(1πx) + 3) - 3| + 2) - 1)) between the vertical lines x = 1.7 and x = 1.9. 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_147
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (3(2(4(-2|(-4x - 3) + 2| + 2)^2 + 4(-2|(-4x - 3) + 2| + 2) - 5)^2 + 2(4(-2|(-4x - 3) + 2| + 2)^2 + 4(-2|(-4x - 3) + 2| + 2) - 5)) + 2)/(-2(2(4(-2|(-4x - 3) + 2| + 2)^2 + 4(-2|(-4x - 3) + 2| + 2) - 5)^2 + 2(4(-2|(-4x - 3) + 2| + 2)^2 + 4(-2|(-4x - 3) + 2| + 2) - 5)) + 3) and g(x) = -3|(-4(3(-3|x + 1|) + 1) - 4) + 1| + 2 from x = -0.8 to x = -0.7000000000000001. 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_148
|
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|(-3|(1x^2 - 4x + 3) - 2| + 3) - 3| + 2) - 1)/(-1(-2|(-3|(1x^2 - 4x + 3) - 2| + 3) - 3| + 2))) + 2 and g(x) = 5((2(3|((-1x + 3)/(2x)) - 3| + 3) + 1)/(2(3|((-1x + 3)/(2x)) - 3| + 3) + 1))^2 + 4((2(3|((-1x + 3)/(2x)) - 3| + 3) + 1)/(2(3|((-1x + 3)/(2x)) - 3| + 3) + 1)) + 4 between the vertical lines x = 3.6 and x = 3.8. Round 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_149
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1(-3|(1|(-1(2e^(2x) + 1) + 2) - 1| - 2) - 2| + 2)^2 + 5(-3|(1|(-1(2e^(2x) + 1) + 2) - 1| - 2) - 2| + 2) - 2 and g(x) = 4(1e^(-1(1|(-1x + 1) - 1|)) - 1)^2 - 4(1e^(-1(1|(-1x + 1) - 1|)) - 1) - 1 from x = 0.3 to x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_4_4_150
|
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(1(3(1|(2x^2 + 2x + 3) - 3| - 1) + 4)^2 - 2(3(1|(2x^2 + 2x + 3) - 3| - 1) + 4) - 1) + 1 and g(x) = 3|((3((-2(1x^2 - 4) - 2)/(-3(1x^2 - 4) - 1)) + 3)/(-3((-2(1x^2 - 4) - 2)/(-3(1x^2 - 4) - 1)) - 3)) + 3| - 1 between the vertical lines x = -1.2 and x = -0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.6
|
math
|
train
|
math_algebra_func_area_level_4_4_151
|
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|(-2cos(3π(1|(4x^2 + 1x - 5) - 3| - 1))) - 1| - 1) - 3)/(2(3|(-2cos(3π(1|(4x^2 + 1x - 5) - 3| - 1))) - 1| - 1) + 3), g(x) = (-2(3|(5(-4x + 4)^2 + 1(-4x + 4) - 3)| - 2) - 1)/(-1(3|(5(-4x + 4)^2 + 1(-4x + 4) - 3)| - 2)), x = 0.8, and x = 1.2. 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_152
|
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(2|(4(-5x + 5) - 2) - 2| - 3)^2 - 5(2|(4(-5x + 5) - 2) - 2| - 3) + 1) + 1| - 1, g(x) = 1(-1(-3|(2|x|)| - 1) - 1)^2 + 2(-1(-3|(2|x|)| - 1) - 1) - 3, x = 0.6, and x = 0.8. Round your answer 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_153
|
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|(-3sin(2π(4(-4x^2 - 3x - 4) + 3) - 3) + 1)| - 2) - 2)/(3(-1|(-3sin(2π(4(-4x^2 - 3x - 4) + 3) - 3) + 1)| - 2)), g(x) = -3|(3|(-4(-1x^2 - 3x + 3) - 2) + 3| + 1) - 1| + 2, x = 0.7, and x = 0.8. 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_154
|
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(3cos(2π(4((-2x + 3)/(-2x - 2))^2 + 4)) - 2)^2 - 3(3cos(2π(4((-2x + 3)/(-2x - 2))^2 + 4)) - 2) - 4) + 2| - 2 and g(x) = 1(2sin(2π(3(-1x + 2) + 2) + 1) + 1) + 3 between the vertical lines x = -1.5 and x = -1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4.1
|
math
|
train
|
math_algebra_func_area_level_4_4_155
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 4(3|(-4((-1(-2|x - 1| + 3) + 3)/(-3(-2|x - 1| + 3) - 2))^2 + 4((-1(-2|x - 1| + 3) + 3)/(-3(-2|x - 1| + 3) - 2))) + 1| - 3)^2 + 1(3|(-4((-1(-2|x - 1| + 3) + 3)/(-3(-2|x - 1| + 3) - 2))^2 + 4((-1(-2|x - 1| + 3) + 3)/(-3(-2|x - 1| + 3) - 2))) + 1| - 3) + 1 and g(x) = (3(5(-2(1x^2 - 2x - 5) + 1)^2 - 3(-2(1x^2 - 2x - 5) + 1) + 2) + 1)/(3(5(-2(1x^2 - 2x - 5) + 1)^2 - 3(-2(1x^2 - 2x - 5) + 1) + 2) + 3) between the vertical lines x = 0.0 and x = 0.1. 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_156
|
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|(-2x + 2)|) + 2) + 2|))/(-3(-1|(2(-1|(-2x + 2)|) + 2) + 2|) - 2) and g(x) = 1e^(1(1(1(-5x^2 + 2) + 5) - 4)) + 3 between the vertical lines x = 1.8 and x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
9.9
|
math
|
train
|
math_algebra_func_area_level_4_4_157
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 4(-1|((3(3((-2x)/(2x + 1))^2 - 1((-2x)/(2x + 1)) + 3))/(-3(3((-2x)/(2x + 1))^2 - 1((-2x)/(2x + 1)) + 3) - 1)) + 3|) + 5 and g(x) = 2|(-5(-1cos(2π(-1x + 2) + 2) + 3) - 2) - 1| - 1 from x = -3 to x = 3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
229.1
|
math
|
train
|
math_algebra_func_area_level_4_4_158
|
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|(-1(-1|(3cos(2π(-1x) - 3) + 1) + 3|)^2 - 1(-1|(3cos(2π(-1x) - 3) + 1) + 3|) + 1) + 3| - 1 and g(x) = 1((-3((1((3x - 2)/(1x + 1)) + 3)/(-3((3x - 2)/(1x + 1)) - 1)) - 3)/(-1((1((3x - 2)/(1x + 1)) + 3)/(-3((3x - 2)/(1x + 1)) - 1)) + 3)) - 4 between the vertical lines x = -2.1 and x = -1.8. 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_159
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1e^(-2(3(4(3((-1x + 3)/(3x + 1))^2 - 4((-1x + 3)/(3x + 1)) + 3)^2 + 3(3((-1x + 3)/(3x + 1))^2 - 4((-1x + 3)/(3x + 1)) + 3) - 1) + 5)) and g(x) = -3|(1cos(1π(-4(-1x^2 - 5x - 3) - 4) - 3))| + 3 from x = 1.7 to x = 1.8. 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_160
|
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((-3((1x - 3)/(2x - 3)) + 1)/(-2((1x - 3)/(2x - 3)) - 2)))) - 3)/(2(-2e^(-1((-3((1x - 3)/(2x - 3)) + 1)/(-2((1x - 3)/(2x - 3)) - 2)))) + 1)) + 2| + 2, g(x) = -1|(1sin(2π(-2|(-1|x + 3| + 1) + 1| + 2) - 2) - 3) + 2| + 1, x = -3.2, and x = -2.8. 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_161
|
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(-2(5(-1x^2 + 3x - 3)^2 - 5(-1x^2 + 3x - 3) + 2) + 1) - 3)/(-3(-2(5(-1x^2 + 3x - 3)^2 - 5(-1x^2 + 3x - 3) + 2) + 1) + 1)) - 2, g(x) = (2(2|(-3|(1x^2 + 3x - 3) - 2| - 3) - 1| - 3) - 1)/(-2(2|(-3|(1x^2 + 3x - 3) - 2| - 3) - 1| - 3) - 2), x = 1.0, and x = 1.6. 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_162
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -1|(1sin(3π(3(-2(-4x + 1)^2 - 3(-4x + 1) - 1)^2 + 3(-2(-4x + 1)^2 - 3(-4x + 1) - 1) + 5) + 1) - 1) - 3| + 1, g(x) = (-1(3cos(1π((1(-1x^2 - 1) - 2)/(2(-1x^2 - 1) + 3)) - 2)))/(3(3cos(1π((1(-1x^2 - 1) - 2)/(2(-1x^2 - 1) + 3)) - 2)) + 1), x = 0.6, 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_163
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 3((-1(-3(1|((-3x + 3)/(2x + 2)) + 3| + 2)))/(2(-3(1|((-3x + 3)/(2x + 2)) + 3| + 2)) - 3)) + 5 and g(x) = (1((1(-3(-3|x - 1| + 3)^2 + 4(-3|x - 1| + 3) + 5) + 1)/(1(-3(-3|x - 1| + 3)^2 + 4(-3|x - 1| + 3) + 5))) + 3)/(-3((1(-3(-3|x - 1| + 3)^2 + 4(-3|x - 1| + 3) + 5) + 1)/(1(-3(-3|x - 1| + 3)^2 + 4(-3|x - 1| + 3) + 5))) - 2) from x = -0.3 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4.5
|
math
|
train
|
math_algebra_func_area_level_4_4_164
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -4(-1|(2cos(2π(-5(-2|x + 3| + 1) - 5) - 2)) - 2| - 1)^2 + 3 and g(x) = -1|(3(-2|((1x - 3)/(-2x)) - 3| - 1) - 2) + 1| + 2 from x = -4.4 to x = -4.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.1
|
math
|
train
|
math_algebra_func_area_level_4_4_165
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -4(-3((2(-2(-1cos(3πx - 2)) + 3) - 3)/(1(-2(-1cos(3πx - 2)) + 3) - 2)) + 5) - 3 and g(x) = -5((2(2|(3x + 4) - 2| + 2) - 1)/(1(2|(3x + 4) - 2| + 2) - 2)) - 2 from x = 4.5 to x = 4.6. 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_166
|
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(1(-1cos(3π(2(-1x^2 - 1x - 4)^2 - 5(-1x^2 - 1x - 4) + 1)) - 2) - 1)^2 - 3(1(-1cos(3π(2(-1x^2 - 1x - 4)^2 - 5(-1x^2 - 1x - 4) + 1)) - 2) - 1) + 1 and g(x) = -1(1(-3e^(-2((-1x - 2)/(3x + 2))))^2 - 1(-3e^(-2((-1x - 2)/(3x + 2)))) + 1)^2 - 1(1(-3e^(-2((-1x - 2)/(3x + 2))))^2 - 1(-3e^(-2((-1x - 2)/(3x + 2)))) + 1) + 3 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}"
]
}
|
1.7
|
math
|
train
|
math_algebra_func_area_level_4_4_167
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 3cos(1π(-2|((2(-5((2x)/(3x + 2)) + 3) - 3)/(-3(-5((2x)/(3x + 2)) + 3) + 2))| + 3) - 3) - 2 and g(x) = -2|(-3|(-3(-2e^(-2x))^2 + 5(-2e^(-2x)) + 2) + 1| + 2) + 3| - 2 from x = 1.1 to x = 1.2000000000000002. 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_168
|
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((2((-2x)/(2x + 3)) + 3)/(1((-2x)/(2x + 3)) + 2))^2 + 4((2((-2x)/(2x + 3)) + 3)/(1((-2x)/(2x + 3)) + 2)) - 2)^2 - 1(-3((2((-2x)/(2x + 3)) + 3)/(1((-2x)/(2x + 3)) + 2))^2 + 4((2((-2x)/(2x + 3)) + 3)/(1((-2x)/(2x + 3)) + 2)) - 2) - 1) - 3)/(-3(3(-3((2((-2x)/(2x + 3)) + 3)/(1((-2x)/(2x + 3)) + 2))^2 + 4((2((-2x)/(2x + 3)) + 3)/(1((-2x)/(2x + 3)) + 2)) - 2)^2 - 1(-3((2((-2x)/(2x + 3)) + 3)/(1((-2x)/(2x + 3)) + 2))^2 + 4((2((-2x)/(2x + 3)) + 3)/(1((-2x)/(2x + 3)) + 2)) - 2) - 1) - 2) and g(x) = 1(3((-2(-2x^2 - 1))/(3(-2x^2 - 1) + 2))^2 + 3((-2(-2x^2 - 1))/(3(-2x^2 - 1) + 2)) - 3)^2 - 5(3((-2(-2x^2 - 1))/(3(-2x^2 - 1) + 2))^2 + 3((-2(-2x^2 - 1))/(3(-2x^2 - 1) + 2)) - 3) - 2 between the vertical lines x = -0.3 and x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.3
|
math
|
train
|
math_algebra_func_area_level_4_4_169
|
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((2x - 3)/(2x)) - 2) - 1| + 2) + 1)/(1(-1|(-3((2x - 3)/(2x)) - 2) - 1| + 2) - 2)) + 2)/(2((-2(-1|(-3((2x - 3)/(2x)) - 2) - 1| + 2) + 1)/(1(-1|(-3((2x - 3)/(2x)) - 2) - 1| + 2) - 2)) + 1) and g(x) = -3|(1(-5(5x + 3)^2 - 1(5x + 3) - 5) + 5) + 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}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_4_4_170
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (1(3(2|((1(1x^2 + 4x) + 2)/(-2(1x^2 + 4x))) + 1| - 3)^2 + 1(2|((1(1x^2 + 4x) + 2)/(-2(1x^2 + 4x))) + 1| - 3) + 4))/(2(3(2|((1(1x^2 + 4x) + 2)/(-2(1x^2 + 4x))) + 1| - 3)^2 + 1(2|((1(1x^2 + 4x) + 2)/(-2(1x^2 + 4x))) + 1| - 3) + 4) - 3) and g(x) = (-1(1(3sin(1π((2x + 3)/(2x - 1)) + 3) + 1) - 4) + 3)/(-2(1(3sin(1π((2x + 3)/(2x - 1)) + 3) + 1) - 4) + 3) from x = -3.8 to x = -2.8. 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_171
|
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(5(1(-5x + 2) - 3) + 3)^2 + 4(5(1(-5x + 2) - 3) + 3) + 2))/(2(-2(5(1(-5x + 2) - 3) + 3)^2 + 4(5(1(-5x + 2) - 3) + 3) + 2) - 1) and g(x) = (-1(-2e^(-2(1|((-1x - 3)/(2x)) + 1|)) + 2) + 2)/(2(-2e^(-2(1|((-1x - 3)/(2x)) + 1|)) + 2) + 2) 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}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_4_4_172
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 3(-2|(3sin(3π(1(-4x - 2) - 2) + 2) - 1)|)^2 + 4(-2|(3sin(3π(1(-4x - 2) - 2) + 2) - 1)|) and g(x) = (1((-3(-1((-2x + 2)/(1x))^2 - 1((-2x + 2)/(1x)) + 4) + 2)/(-2(-1((-2x + 2)/(1x))^2 - 1((-2x + 2)/(1x)) + 4) + 3)) - 1)/(-3((-3(-1((-2x + 2)/(1x))^2 - 1((-2x + 2)/(1x)) + 4) + 2)/(-2(-1((-2x + 2)/(1x))^2 - 1((-2x + 2)/(1x)) + 4) + 3)) - 2) from x = 4.1 to x = 4.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.8
|
math
|
train
|
math_algebra_func_area_level_4_4_173
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 3(-2|(-2cos(2π(5(2|x - 3|)^2 + 4(2|x - 3|) + 2) + 3) + 3) - 3| + 3)^2 - 2(-2|(-2cos(2π(5(2|x - 3|)^2 + 4(2|x - 3|) + 2) + 3) + 3) - 3| + 3) - 4 and g(x) = (2(2|(-2e^(1((-1x - 2)/(1x + 3))) + 3) - 1| + 1) + 2)/(2(2|(-2e^(1((-1x - 2)/(1x + 3))) + 3) - 1| + 1) + 2) from x = -3.8 to x = -3.6999999999999997. 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_174
|
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|((1(-5(-5(-1|x - 3| + 3)) + 1) - 2)/(-3(-5(-5(-1|x - 3| + 3)) + 1) + 2)) + 2| - 2 and g(x) = (-1((-1(2e^(-1(-4x + 1)) + 3) + 1)/(-2(2e^(-1(-4x + 1)) + 3) + 3)))/(1((-1(2e^(-1(-4x + 1)) + 3) + 1)/(-2(2e^(-1(-4x + 1)) + 3) + 3)) - 2) between the vertical lines x = -0.0 and x = 0.1. 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_175
|
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|(2|(1|((-2(3cos(1πx + 2) + 2) - 1)/(-2(3cos(1πx + 2) + 2) - 2))|) + 2| + 1) - 2| - 2 and g(x) = 2|(2|((-3(3e^(-2x) + 1) + 2)/(2(3e^(-2x) + 1) + 2)) - 1| + 1) - 1| - 2 between the vertical lines x = -1.5 and x = -1.4. 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_176
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 4((-3(1|(1|((-3x - 2)/(-1x + 2)) + 3| + 2) - 3| + 1) + 3)/(-3(1|(1|((-3x - 2)/(-1x + 2)) + 3| + 2) - 3| + 1))) + 2 and g(x) = (-3(-2|(-5(1sin(1πx - 1) + 3)^2 - 4(1sin(1πx - 1) + 3))| - 1) - 1)/(-1(-2|(-5(1sin(1πx - 1) + 3)^2 - 4(1sin(1πx - 1) + 3))| - 1)) from x = 0.3 to x = 0.5. 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_177
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 2cos(3π(-5(4(-3((-3x - 1)/(3x + 3)) - 2) - 4) - 3) - 2) + 3 and g(x) = -2((-2((2(-2x^2 + 2x - 1) + 3)/(2(-2x^2 + 2x - 1) + 1)) - 3)/(1((2(-2x^2 + 2x - 1) + 3)/(2(-2x^2 + 2x - 1) + 1)) + 3))^2 - 5((-2((2(-2x^2 + 2x - 1) + 3)/(2(-2x^2 + 2x - 1) + 1)) - 3)/(1((2(-2x^2 + 2x - 1) + 3)/(2(-2x^2 + 2x - 1) + 1)) + 3)) + 4 from x = 0.3 to x = 0.4. 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_178
|
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(-1x + 4) - 1)/(-2(-1x + 4) - 2)) + 1|) - 3)/(3(1|((2(-1x + 4) - 1)/(-2(-1x + 4) - 2)) + 1|) + 3)) - 2)/(2((-2(1|((2(-1x + 4) - 1)/(-2(-1x + 4) - 2)) + 1|) - 3)/(3(1|((2(-1x + 4) - 1)/(-2(-1x + 4) - 2)) + 1|) + 3)) + 3), g(x) = -3(4(-5(-4x + 5)^2 - 2(-4x + 5) + 5)^2 + 4(-5(-4x + 5)^2 - 2(-4x + 5) + 5)) + 4, x = 1.0, and x = 1.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
107.0
|
math
|
train
|
math_algebra_func_area_level_4_4_179
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -3(3sin(1π(-3(1((-2x)/(-1x + 2))^2 + 1((-2x)/(-1x + 2)) - 1) - 2) - 1) - 3)^2 - 5(3sin(1π(-3(1((-2x)/(-1x + 2))^2 + 1((-2x)/(-1x + 2)) - 1) - 2) - 1) - 3) - 3 and g(x) = (-3(-3((-2((-1x + 1)/(-2x)) + 1)/(1((-1x + 1)/(-2x)) - 3))^2 + 4((-2((-1x + 1)/(-2x)) + 1)/(1((-1x + 1)/(-2x)) - 3)) + 4))/(2(-3((-2((-1x + 1)/(-2x)) + 1)/(1((-1x + 1)/(-2x)) - 3))^2 + 4((-2((-1x + 1)/(-2x)) + 1)/(1((-1x + 1)/(-2x)) - 3)) + 4) + 2) from x = -0.0 to x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_4_4_180
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (2((1((-1(-3|(-3|x - 2| - 2) + 3| + 1) - 1)/(1(-3|(-3|x - 2| - 2) + 3| + 1) + 3)) + 2)/(-1((-1(-3|(-3|x - 2| - 2) + 3| + 1) - 1)/(1(-3|(-3|x - 2| - 2) + 3| + 1) + 3)))) + 1)/(-1((1((-1(-3|(-3|x - 2| - 2) + 3| + 1) - 1)/(1(-3|(-3|x - 2| - 2) + 3| + 1) + 3)) + 2)/(-1((-1(-3|(-3|x - 2| - 2) + 3| + 1) - 1)/(1(-3|(-3|x - 2| - 2) + 3| + 1) + 3))))), g(x) = 1sin(2π(-2|(-2((-1x - 2)/(2x + 3))^2 + 4((-1x - 2)/(2x + 3)) + 1) - 3| + 3)), x = 1.2, and x = 2.9. Round your answer 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_181
|
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(-5(2(3|x + 2| + 2) - 5)^2 - 5(2(3|x + 2| + 2) - 5) - 1))/(-3(-5(2(3|x + 2| + 2) - 5)^2 - 5(2(3|x + 2| + 2) - 5) - 1) - 1)) - 4, g(x) = (1(5(-3|(2sin(2πx - 3) - 1) + 3| + 2) - 1) - 2)/(1(5(-3|(2sin(2πx - 3) - 1) + 3| + 2) - 1) + 3), x = 1.4, and x = 2.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4.1
|
math
|
train
|
math_algebra_func_area_level_4_4_182
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 2|(1((3(-1|((1x - 3)/(2x + 1)) + 2| - 2) - 2)/(3(-1|((1x - 3)/(2x + 1)) + 2| - 2) - 1))^2 - 3((3(-1|((1x - 3)/(2x + 1)) + 2| - 2) - 2)/(3(-1|((1x - 3)/(2x + 1)) + 2| - 2) - 1)) - 2) - 2| + 1 and g(x) = -3((-2(2|(3|x + 3| - 3) - 3| - 1))/(3(2|(3|x + 3| - 3) - 3| - 1) + 2)) - 5 from x = -5.0 to x = -1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
83.4
|
math
|
train
|
math_algebra_func_area_level_4_4_183
|
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(2e^(-1(5((-2x + 3)/(-2x + 3))^2 + 5((-2x + 3)/(-2x + 3)) - 5)) + 3) + 3)/(-3(2e^(-1(5((-2x + 3)/(-2x + 3))^2 + 5((-2x + 3)/(-2x + 3)) - 5)) + 3) - 2)) - 3 and g(x) = -3(-1sin(2π(-4(2|x - 1| - 3)^2 + 3(2|x - 1| - 3) + 1) + 1) - 2)^2 - 4(-1sin(2π(-4(2|x - 1| - 3)^2 + 3(2|x - 1| - 3) + 1) + 1) - 2) + 2 between the vertical lines x = -0.1 and x = 0.0. 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_184
|
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(-3sin(1π(-2x + 1) - 2))^2 - 5(-3sin(1π(-2x + 1) - 2))) - 2)/(-3(1(-3sin(1π(-2x + 1) - 2))^2 - 5(-3sin(1π(-2x + 1) - 2))) - 1)) + 1, g(x) = -1(1|(-2|(-1x^2 - 1x + 2) + 1| - 3) + 3|)^2 - 2(1|(-2|(-1x^2 - 1x + 2) + 1| - 3) + 3|) - 1, x = -2.3, and x = 1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
117.2
|
math
|
train
|
math_algebra_func_area_level_4_4_185
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -1|(4(2|(4(1|x - 2| + 1) - 2) - 1|)^2 + 3(2|(4(1|x - 2| + 1) - 2) - 1|) + 2) - 1|, g(x) = -3(-4(-1(4x - 1) - 4) + 4) + 4, x = 1.6, and x = 2.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
60.2
|
math
|
train
|
math_algebra_func_area_level_4_4_186
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -5(1|(-1((1(4x^2 + 5x + 5) - 1)/(3(4x^2 + 5x + 5) - 2)) + 3) + 1| - 2)^2 - 1(1|(-1((1(4x^2 + 5x + 5) - 1)/(3(4x^2 + 5x + 5) - 2)) + 3) + 1| - 2) + 1 and g(x) = (3((-1(-5(1x^2 + 2x + 1)^2 + 1) - 2)/(-3(-5(1x^2 + 2x + 1)^2 + 1) + 4)) - 1)/(-1((-1(-5(1x^2 + 2x + 1)^2 + 1) - 2)/(-3(-5(1x^2 + 2x + 1)^2 + 1) + 4))) from x = -1.8 to x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
17.5
|
math
|
train
|
math_algebra_func_area_level_4_4_187
|
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|(4(-2((3x - 1)/(3x - 1))^2 - 2((3x - 1)/(3x - 1)) + 3) - 5) + 2| + 3) + 1| - 1, g(x) = 1|(1(-1(3|x| - 1)^2 - 5(3|x| - 1) - 4)^2 + 5(-1(3|x| - 1)^2 - 5(3|x| - 1) - 4)) - 1| - 1, x = -0.5, and x = 0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4.1
|
math
|
train
|
math_algebra_func_area_level_4_4_188
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3e^(-2(4((3(3(2x + 2)^2 - 3(2x + 2) - 2) - 3)/(-2(3(2x + 2)^2 - 3(2x + 2) - 2) + 1))^2 + 2)) + 3, g(x) = (-2((-2(-2|(3|x + 1| + 3) - 2| + 3) - 2)/(2(-2|(3|x + 1| + 3) - 2| + 3) - 3)) - 3)/(-2((-2(-2|(3|x + 1| + 3) - 2| + 3) - 2)/(2(-2|(3|x + 1| + 3) - 2| + 3) - 3)) + 1), x = -1.1, and x = -0.9. 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_189
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1(-1(2(3((2x + 1)/(2x)) - 5) + 3))^2 + 3(-1(2(3((2x + 1)/(2x)) - 5) + 3)) - 3 and g(x) = -5(3|(-1(3x)) - 3| - 1)^2 - 5(3|(-1(3x)) - 3| - 1) + 5 from x = -0.7 to x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
21.7
|
math
|
train
|
math_algebra_func_area_level_4_4_190
|
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(-4(-3|(-5x^2 + 5x + 3) - 3| + 3) + 4))/(-2(-4(-3|(-5x^2 + 5x + 3) - 3| + 3) + 4) + 3)) + 1| - 1 and g(x) = (-3(-2(1sin(1π(-1x - 1) - 1) + 3) - 1) - 3)/(3(-2(1sin(1π(-1x - 1) - 1) + 3) - 1) + 3) between the vertical lines x = 0.1 and x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
10.3
|
math
|
train
|
math_algebra_func_area_level_4_4_191
|
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(1π(1((-3(-3(-3x - 2) - 5) - 3)/(2(-3(-3x - 2) - 5) + 1))^2 + 2((-3(-3(-3x - 2) - 5) - 3)/(2(-3(-3x - 2) - 5) + 1)) + 1) - 3) + 1 and g(x) = -2((-2(-2((1x - 3)/(3x - 1))) - 1)/(-3(-2((1x - 3)/(3x - 1))) + 2))^2 + 3((-2(-2((1x - 3)/(3x - 1))) - 1)/(-3(-2((1x - 3)/(3x - 1))) + 2)) - 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}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_4_4_192
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -3e^(-1(5((-1(2|(1x + 3) + 2| - 2) - 1)/(1(2|(1x + 3) + 2| - 2) + 3))^2 - 4((-1(2|(1x + 3) + 2| - 2) - 1)/(1(2|(1x + 3) + 2| - 2) + 3)) - 5)) + 2, g(x) = 2|(-3cos(3π((2(1x^2 + 4) + 3)/(-3(1x^2 + 4) - 1)) - 3))| - 1, x = -1.0, and x = 1.2. 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_193
|
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(-2sin(2π(4x^2 + 4x + 1) - 1) - 2) - 2)/(1(-2sin(2π(4x^2 + 4x + 1) - 1) - 2))) - 1| + 1))/(-3(-1|((-2(-2sin(2π(4x^2 + 4x + 1) - 1) - 2) - 2)/(1(-2sin(2π(4x^2 + 4x + 1) - 1) - 2))) - 1| + 1) + 4), g(x) = 1(2(5((-3x + 3)/(1x))^2 - 1((-3x + 3)/(1x))) - 5) + 3, x = 1.0, and x = 1.1. 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_194
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -2|(-5(2sin(2π(1((2x - 3)/(-3x + 2)) - 2)) - 1) + 2) + 2| + 3, g(x) = 2|(-3cos(1π(3|((1x + 1)/(-1x + 2)) + 1| - 3)) + 1) - 3| + 1, x = 0.4, and x = 0.5. 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_195
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1(-5((1(-3|(-5x + 2) - 3|) - 1)/(2(-3|(-5x + 2) - 3|) - 3)) + 2) + 5 and g(x) = 4(1|((2(2e^(-1x) + 3) - 2)/(3(2e^(-1x) + 3) + 1))|) + 3 from x = -1.9 to x = -0.3. 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_196
|
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(-5(-1((1x + 3)/(3x - 2))^2 + 1((1x + 3)/(3x - 2)) + 3)^2 + 1(-1((1x + 3)/(3x - 2))^2 + 1((1x + 3)/(3x - 2)) + 3) - 1)^2 + 1(-5(-1((1x + 3)/(3x - 2))^2 + 1((1x + 3)/(3x - 2)) + 3)^2 + 1(-1((1x + 3)/(3x - 2))^2 + 1((1x + 3)/(3x - 2)) + 3) - 1) - 5))/(-1(3(-5(-1((1x + 3)/(3x - 2))^2 + 1((1x + 3)/(3x - 2)) + 3)^2 + 1(-1((1x + 3)/(3x - 2))^2 + 1((1x + 3)/(3x - 2)) + 3) - 1)^2 + 1(-5(-1((1x + 3)/(3x - 2))^2 + 1((1x + 3)/(3x - 2)) + 3)^2 + 1(-1((1x + 3)/(3x - 2))^2 + 1((1x + 3)/(3x - 2)) + 3) - 1) - 5) + 2) and g(x) = -1(3|(-1e^(-1(3x^2 - 1x - 3))) - 2| + 3) + 1 between the vertical lines x = -0.2 and x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
63.9
|
math
|
train
|
math_algebra_func_area_level_4_4_197
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -2sin(2π(-1|(-5(2|(-1x^2 - 5x - 2) - 1| - 3) - 1) + 2| - 3) - 3) + 1 and g(x) = -1|((1((-3(5x + 4) - 2)/(2(5x + 4) - 1)) + 1)/(-2((-3(5x + 4) - 2)/(2(5x + 4) - 1)) + 1)) + 1| + 3 from x = 0.3 to x = 0.4. 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_198
|
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(4x) + 2)/(2(4x) - 1)) + 2)/(-3((1(4x) + 2)/(2(4x) - 1)))) - 1| - 3), g(x) = (-3(-1cos(2π(-1|((1x - 2)/(1x + 1)) - 3| + 1) - 1) + 3) + 2)/(-3(-1cos(2π(-1|((1x - 2)/(1x + 1)) - 3| + 1) - 1) + 3) + 1), x = -0.4, and x = 4.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
9.4
|
math
|
train
|
math_algebra_func_area_level_4_4_199
|
algebra_func_area4
|
hard (level 4,5)
| 4 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 3|((-2(1(5(3|x - 2| - 1) + 3) + 5) - 3)/(2(1(5(3|x - 2| - 1) + 3) + 5) + 1)) - 1| + 2 and g(x) = 1|(-1(-2e^(-1(2|x - 1|)) + 2)^2 - 4(-2e^(-1(2|x - 1|)) + 2) + 5) - 1| + 2 from x = -0.0 to x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
6.3
|
math
|
train
|
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