id
string | setting_key
string | difficulty
string | level
int32 | messages
dict | ground_truth
string | dataset
string | omega_split
string |
|---|---|---|---|---|---|---|---|
math_algebra_func_area_level_3_3_100
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -3(-3|(-1|(1cos(3πx - 1) + 3) + 1| - 3) - 1| - 3), g(x) = 1(-4((3x + 2)/(-1x))^2 + 1((3x + 2)/(-1x)))^2 - 5, x = -1.3, and x = -0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
54.9
|
math
|
train
|
math_algebra_func_area_level_3_3_101
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 1|(-1((-2(-1|x + 3| - 2) - 3)/(-2(-1|x + 3| - 2) + 3))^2 + 2((-2(-1|x + 3| - 2) - 3)/(-2(-1|x + 3| - 2) + 3)) + 2)| and g(x) = 1sin(1π(-1(-2|x + 3| - 1) + 5) + 2) + 3 between the vertical lines x = -4.2 and x = -3.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.6
|
math
|
train
|
math_algebra_func_area_level_3_3_102
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 1((3(1|(-1e^(-1x) + 2) - 3| - 1) - 1)/(-2(1|(-1e^(-1x) + 2) - 3| - 1) - 3)), g(x) = -1|(1cos(3π((-3x - 3)/(1x + 2)) - 2) - 3) + 1| + 2, x = -1.3, and x = -1.2. 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_3_3_103
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-2(-4(1(-4x^2 + 3)^2 - 3(-4x^2 + 3) - 1)^2 - 5))/(3(-4(1(-4x^2 + 3)^2 - 3(-4x^2 + 3) - 1)^2 - 5) + 3), g(x) = -1(1|(1x^2 - 1x - 1) - 3| + 3)^2 + 3(1|(1x^2 - 1x - 1) - 3| + 3), x = -1.5, and x = 2.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
72.0
|
math
|
train
|
math_algebra_func_area_level_3_3_104
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -5(1cos(3π(2(2x^2 + 5x + 2)^2 + 5(2x^2 + 5x + 2) - 1) - 3) - 1)^2 + 5(1cos(3π(2(2x^2 + 5x + 2)^2 + 5(2x^2 + 5x + 2) - 1) - 3) - 1) + 4 and g(x) = -1|(5((-2x + 3)/(-3x + 4)) - 1) - 3| - 3 between the vertical lines x = -4.2 and x = -4.1000000000000005. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.9
|
math
|
train
|
math_algebra_func_area_level_3_3_105
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -2|(3|(-4(-1cos(3πx + 1)) + 1) + 1| + 1)| + 2 and g(x) = (2(2|(1|x + 1|) + 2| + 2) + 2)/(-2(2|(1|x + 1|) + 2| + 2)) between the vertical lines x = 0.8 and x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.8
|
math
|
train
|
math_algebra_func_area_level_3_3_106
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -5((-2(-2cos(3π(2x^2 - 1x - 3) - 1) + 3) + 1)/(1(-2cos(3π(2x^2 - 1x - 3) - 1) + 3) + 1))^2 + 3((-2(-2cos(3π(2x^2 - 1x - 3) - 1) + 3) + 1)/(1(-2cos(3π(2x^2 - 1x - 3) - 1) + 3) + 1)) - 4, g(x) = -1e^(2(4((-2x)/(2x + 2))^2 - 1((-2x)/(2x + 2)))) - 3, x = 0.9, and x = 1.0. 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_3_3_107
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -4(3e^(2((-2(2x + 5) + 2)/(-2(2x + 5)))) - 2)^2 - 1(3e^(2((-2(2x + 5) + 2)/(-2(2x + 5)))) - 2) + 2, g(x) = -3|(2cos(2π((-3x - 2)/(-2x + 3)))) - 3|, x = -2.4, and x = -1.9. 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_3_3_108
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 2|((-1((3(3|x| + 3) - 2)/(1(3|x| + 3) - 2)) + 2)/(2((3(3|x| + 3) - 2)/(1(3|x| + 3) - 2)) - 3))| - 2 and g(x) = 1sin(1π(-2((-3x + 3)/(2x - 1)) - 2) - 3) - 1 from x = 0.4 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_3_3_109
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -1((-1(-3(1x + 3)^2 - 4(1x + 3) - 1) + 2)/(3(-3(1x + 3)^2 - 4(1x + 3) - 1))) - 3 and g(x) = (-1(2(1x^2 + 1x + 1)^2 + 3(1x^2 + 1x + 1) + 5) - 3)/(-1(2(1x^2 + 1x + 1)^2 + 3(1x^2 + 1x + 1) + 5) + 3) between the vertical lines x = -4.1 and x = -3.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
21.5
|
math
|
train
|
math_algebra_func_area_level_3_3_110
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3|((3((2((1x + 1)/(3x + 1)))/(2((1x + 1)/(3x + 1)) - 1)) + 3)/(2((2((1x + 1)/(3x + 1)))/(2((1x + 1)/(3x + 1)) - 1)))) + 2| - 1, g(x) = (1(-2|(-1sin(3πx + 1) - 1) + 3| + 1) - 1)/(1(-2|(-1sin(3πx + 1) - 1) + 3| + 1)), x = -1.8, and x = -1.4. 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_3_3_111
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-1(-1|(-1|(2x + 4) - 1|) - 3|) + 3)/(-2(-1|(-1|(2x + 4) - 1|) - 3|) + 1), g(x) = 2|(-4(-3x) + 4) - 1|, x = -0.3, and x = -0.2. 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_3_3_112
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-2(-2sin(3π((3(3|x + 2| - 2) + 2)/(3(3|x + 2| - 2) + 1)) + 1) - 1))/(3(-2sin(3π((3(3|x + 2| - 2) + 2)/(3(3|x + 2| - 2) + 1)) + 1) - 1) - 2), g(x) = (-3((-1(1x^2 - 5x + 3))/(-1(1x^2 - 5x + 3) - 3)) - 3)/(1((-1(1x^2 - 5x + 3))/(-1(1x^2 - 5x + 3) - 3)) - 2), x = -2.5, and x = -2.4. 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_3_3_113
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -3cos(3π(4(-3(1x + 5) - 5)^2 - 3) - 3) - 1, g(x) = -4(-1|(-2|x| - 1)| + 3) - 5, x = -1.3, and x = -1.2. 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_3_3_114
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -3|(-2cos(2π(3(-3|x + 1|)^2 + 1(-3|x + 1|) - 4) + 2) - 2) + 1| + 1 and g(x) = (1(2sin(1π(-1x + 4) + 3) + 2) - 2)/(3(2sin(1π(-1x + 4) + 3) + 2) - 2) between the vertical lines x = 0.1 and x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.4
|
math
|
train
|
math_algebra_func_area_level_3_3_115
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (1((2(4(-3sin(1πx + 3)) - 1) - 2)/(-3(4(-3sin(1πx + 3)) - 1) - 3)) + 1)/(-1((2(4(-3sin(1πx + 3)) - 1) - 2)/(-3(4(-3sin(1πx + 3)) - 1) - 3)) + 3), g(x) = 4(-5((1x + 3)/(1x))^2 - 3((1x + 3)/(1x)) + 3) - 4, x = -3.0, and x = -1.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
12.2
|
math
|
train
|
math_algebra_func_area_level_3_3_116
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1(1((1(1x^2 - 2x + 4) + 3)/(-1(1x^2 - 2x + 4) + 2)) + 2) - 2 and g(x) = (1(-2|(1|x + 3| + 2) - 2| - 3))/(-3(-2|(1|x + 3| + 2) - 2| - 3) - 3) from x = 0.0 to x = 2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.6
|
math
|
train
|
math_algebra_func_area_level_3_3_117
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -2cos(1π((2(-1((3x - 1)/(2x + 2))^2 - 4((3x - 1)/(2x + 2)) + 4) - 1)/(3(-1((3x - 1)/(2x + 2))^2 - 4((3x - 1)/(2x + 2)) + 4) + 2))) - 1, g(x) = -1|(2cos(2π(-3|x + 2| + 3) - 3) + 3) - 1| + 1, x = 2.7, and x = 2.8000000000000003. 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_3_3_118
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-3(2(-1(-2x - 5)^2 + 1(-2x - 5) + 3)))/(-2(2(-1(-2x - 5)^2 + 1(-2x - 5) + 3)) - 1) and g(x) = -3e^(-2((-2(1x^2 - 4x - 2) - 2)/(-1(1x^2 - 4x - 2) - 1))) - 3 from x = -3.7 to x = -1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
8.7
|
math
|
train
|
math_algebra_func_area_level_3_3_119
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -2cos(3π(-1|(-5(-3|x + 3| + 2)^2 + 3(-3|x + 3| + 2) - 5) - 3|) + 3), g(x) = (1(-2e^(-1(2|x| + 3))) - 1)/(1(-2e^(-1(2|x| + 3))) - 2), x = -3.9, and x = -3.8. 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_3_3_120
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -2e^(-1((-1(2|(4x - 3) - 1| - 1))/(2(2|(4x - 3) - 1| - 1) - 1))) + 3 and g(x) = 1sin(3π(5(4x^2 + 1x + 3)^2 - 1) + 3) - 2 from x = 0.7 to x = 0.7999999999999999. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_3_3_121
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 2sin(2π(3((-2(3x) + 1)/(-3(3x)))^2 + 4((-2(3x) + 1)/(-3(3x))))) and g(x) = 5((-2(-1x^2 + 1x - 5))/(-2(-1x^2 + 1x - 5) - 1))^2 - 4((-2(-1x^2 + 1x - 5))/(-2(-1x^2 + 1x - 5) - 1)) from x = -0.3 to x = -0.19999999999999998. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_3_3_122
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-2(-2(-2|(-1|x - 3|) + 2| + 2) + 2) + 1)/(1(-2(-2|(-1|x - 3|) + 2| + 2) + 2) + 3) and g(x) = 1(-1(-1|x - 3| - 3) + 1) - 2 from x = 1.0 to x = 5.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
12.4
|
math
|
train
|
math_algebra_func_area_level_3_3_123
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 3((2(1cos(2π(-1x - 5) - 2)) + 3)/(3(1cos(2π(-1x - 5) - 2)) + 2)) - 1 and g(x) = 1|(-2|(1|x - 3| - 3) + 2| - 1) - 2| + 3 from x = 4.0 to x = 4.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
9.5
|
math
|
train
|
math_algebra_func_area_level_3_3_124
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -3cos(1π(1(-1|(-1x - 3) - 3|) - 3) + 1) and g(x) = 1(3|(1x^2 - 2x - 3) + 2| - 1)^2 + 5(3|(1x^2 - 2x - 3) + 2| - 1) + 2 between the vertical lines x = 2.3 and x = 2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.7
|
math
|
train
|
math_algebra_func_area_level_3_3_125
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (1(5(2((-1x - 2)/(1x - 3))^2 - 5((-1x - 2)/(1x - 3)) - 4)^2 + 5(2((-1x - 2)/(1x - 3))^2 - 5((-1x - 2)/(1x - 3)) - 4) + 2) + 2)/(-1(5(2((-1x - 2)/(1x - 3))^2 - 5((-1x - 2)/(1x - 3)) - 4)^2 + 5(2((-1x - 2)/(1x - 3))^2 - 5((-1x - 2)/(1x - 3)) - 4) + 2)) and g(x) = 2(2sin(3π(-3x))) - 4 between the vertical lines x = -3.9 and x = -3.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_3_3_126
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 3sin(3π(-4((3(-5x^2 - 5x) - 2)/(2(-5x^2 - 5x) + 2))^2 - 2((3(-5x^2 - 5x) - 2)/(2(-5x^2 - 5x) + 2)) - 4) - 2) + 2 and g(x) = -2(1sin(3π(3|x + 1| - 1) - 2) + 1) + 3 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_3_3_127
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3cos(3π(-1|(5(5x + 1) - 3) + 2| + 2) - 1) + 3, g(x) = 1(4(-5x + 4) + 2)^2 + 3(4(-5x + 4) + 2) + 5, x = 1.0, and x = 1.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_3_3_128
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -2|((-2(1(3e^(-2x) - 2) - 2) + 1)/(-3(1(3e^(-2x) - 2) - 2) + 2)) - 3| + 2, g(x) = (-2(-3|(-2e^(1x) + 2) + 3| + 3) - 2)/(-3(-3|(-2e^(1x) + 2) + 3| + 3) + 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}"
]
}
|
0.4
|
math
|
train
|
math_algebra_func_area_level_3_3_129
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1(-2(2sin(2π((-2x + 1)/(-3x)) - 1) - 2) - 2) - 3 and g(x) = (-1(3|(2cos(1πx - 1) + 3)| - 3))/(-1(3|(2cos(1πx - 1) + 3)| - 3)) from x = -0.0 to x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_3_3_130
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -3(3(-1(1x^2 + 1x - 4) + 4)^2 - 3(-1(1x^2 + 1x - 4) + 4) + 3) - 1 and g(x) = -2|(3(2x^2 - 1x + 1) + 4) + 1| - 2 from x = 1.9 to x = 2.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
37.6
|
math
|
train
|
math_algebra_func_area_level_3_3_131
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 1((-1(-2sin(2π(1|x + 2|) - 1) + 2) + 1)/(1(-2sin(2π(1|x + 2|) - 1) + 2) + 2))^2 + 4((-1(-2sin(2π(1|x + 2|) - 1) + 2) + 1)/(1(-2sin(2π(1|x + 2|) - 1) + 2) + 2)) - 1 and g(x) = -1|(4(-4x + 5)^2 - 3) - 2| - 2 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}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_3_3_132
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 1((1(3|(-3|x + 3| - 3) - 2|))/(2(3|(-3|x + 3| - 3) - 2|) - 1)) - 3, g(x) = -1cos(1π(-2|(-2x + 2) - 1| - 3) - 2) - 3, x = -2.3, and x = -1.9. 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_3_3_133
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -3|((-3(-1(5x^2 - 3x - 4)^2 - 4(5x^2 - 3x - 4) + 1) - 1)/(-3(-1(5x^2 - 3x - 4)^2 - 4(5x^2 - 3x - 4) + 1) - 1)) - 1| - 2, g(x) = 1|(-5(-5x^2 - 5x - 1) + 5) - 3| - 3, x = -0.6, and x = -0.4. 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_3_3_134
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 1(-1|((-1(3cos(2πx + 1)) - 1)/(2(3cos(2πx + 1)) - 1)) - 3| - 2) + 1, g(x) = -3(3cos(3π(-5x + 2)) + 2) - 5, x = 3.8, and x = 3.9. 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_3_3_135
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3|((2(2|(5x^2 + 1) - 2| + 2))/(2(2|(5x^2 + 1) - 2| + 2) + 2)) - 1| + 3, g(x) = -1(-3|(-1|x + 3| - 1) + 3| - 3) - 4, x = -2.4, and x = 0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
6.4
|
math
|
train
|
math_algebra_func_area_level_3_3_136
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -1(1(3(-1x^2 - 5x + 4)^2 - 2(-1x^2 - 5x + 4) + 1)) + 3, g(x) = 2|(3sin(2π((1x + 3)/(1x - 2)) + 3) - 2) + 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}"
]
}
|
0.4
|
math
|
train
|
math_algebra_func_area_level_3_3_137
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (3(2|(-1e^(1(-1x + 4)) - 1)| - 3) - 1)/(-2(2|(-1e^(1(-1x + 4)) - 1)| - 3) + 3) and g(x) = 3e^(-1(2((3x + 3)/(-2x + 3))^2 + 1((3x + 3)/(-2x + 3)) - 1)) - 3 from x = -0.2 to x = 3.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4.4
|
math
|
train
|
math_algebra_func_area_level_3_3_138
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-3(5(-4(-4x - 1)^2 + 3(-4x - 1) - 4)^2 + 3(-4(-4x - 1)^2 + 3(-4x - 1) - 4) + 1) - 1)/(2(5(-4(-4x - 1)^2 + 3(-4x - 1) - 4)^2 + 3(-4(-4x - 1)^2 + 3(-4x - 1) - 4) + 1) - 3) and g(x) = -5(-2(-2|x - 3| + 3) - 1)^2 - 4(-2(-2|x - 3| + 3) - 1) + 1 from x = 1.2 to x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.9
|
math
|
train
|
math_algebra_func_area_level_3_3_139
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-1((1(1(1sin(2πx - 3) + 1)^2 + 3(1sin(2πx - 3) + 1) - 1) - 3)/(-3(1(1sin(2πx - 3) + 1)^2 + 3(1sin(2πx - 3) + 1) - 1) - 2)) + 3)/(-1((1(1(1sin(2πx - 3) + 1)^2 + 3(1sin(2πx - 3) + 1) - 1) - 3)/(-3(1(1sin(2πx - 3) + 1)^2 + 3(1sin(2πx - 3) + 1) - 1) - 2)) - 1), g(x) = -2|(-3((-1x - 3)/(2x + 1)) + 5) + 2|, x = -1.0, and x = -0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_3_3_140
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-1(1|(-1|(2x^2 - 3x + 2) - 3|) + 1| - 1) - 1)/(2(1|(-1|(2x^2 - 3x + 2) - 3|) + 1| - 1) + 3), g(x) = -4(-4(3cos(1πx + 2) - 3) - 2)^2 - 3(-4(3cos(1πx + 2) - 3) - 2) + 4, x = -4.7, and x = -4.5. 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_3_3_141
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 5(3(-3(5x + 3)^2 + 2(5x + 3) + 2) + 5)^2 + 3(3(-3(5x + 3)^2 + 2(5x + 3) + 2) + 5) - 4 and g(x) = -1((2(3|x - 2| - 3))/(2(3|x - 2| - 3) + 1))^2 + 5((2(3|x - 2| - 3))/(2(3|x - 2| - 3) + 1)) + 3 between the vertical lines x = -0.3 and x = -0.19999999999999998. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
23.6
|
math
|
train
|
math_algebra_func_area_level_3_3_142
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 2(-1e^(-2(-1(-3x - 4) + 3))) + 1 and g(x) = -3cos(2π(3|(5x^2 - 2x + 3) - 3| + 3) - 1) from x = 2.3 to x = 2.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_3_3_143
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -1(-3sin(3π(2|((2x + 1)/(3x - 2)) + 3| - 1)) - 1)^2 - 4, g(x) = -3(-1cos(1π((1x - 3)/(-3x)) + 1) + 1)^2 + 1(-1cos(1π((1x - 3)/(-3x)) + 1) + 1) - 4, x = 0.9, and x = 1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.6
|
math
|
train
|
math_algebra_func_area_level_3_3_144
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (2(3e^(-1((-1(1x^2 - 1))/(-2(1x^2 - 1) + 1)))) + 3)/(-1(3e^(-1((-1(1x^2 - 1))/(-2(1x^2 - 1) + 1)))) - 2), g(x) = -2(-2(-3|x + 1| + 3) - 4) - 1, x = -2.7, and x = 0.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
35.9
|
math
|
train
|
math_algebra_func_area_level_3_3_145
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-2(-2|(-2sin(2π(2|x + 1| - 1) - 2) + 1) - 2| + 1) - 2)/(-1(-2|(-2sin(2π(2|x + 1| - 1) - 2) + 1) - 2| + 1) + 3), g(x) = 1|(-2cos(3π(5x^2 + 1x - 2) + 2) + 1) + 2| - 2, x = -3.1, and x = -3.0. 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_3_3_146
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3|(2|(1(-5x^2 - 3x - 2) + 3) + 1| + 3) - 3| + 1, g(x) = 1|(-3|((2x + 2)/(-3x))|) - 1| + 3, x = -1.1, and x = -0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_3_3_147
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 2sin(1π(2|(-1|(5x + 4) + 1| - 3) - 1| - 1)) + 1 and g(x) = (-2(-2(5x^2 - 5x) - 1) - 1)/(-3(-2(5x^2 - 5x) - 1) + 1) between the vertical lines x = 3.6 and x = 3.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_3_3_148
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -2cos(2π((3((-3((-1x + 1)/(-1x - 3)) - 1)/(-1((-1x + 1)/(-1x - 3)) + 3)) + 3)/(3((-3((-1x + 1)/(-1x - 3)) - 1)/(-1((-1x + 1)/(-1x - 3)) + 3)) + 3))) - 2 and g(x) = -3(2|(3|x + 2| - 3) + 2| - 3) + 1 between the vertical lines x = -3.1 and x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
18.2
|
math
|
train
|
math_algebra_func_area_level_3_3_149
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 3sin(2π(-2|(3((-3x - 2)/(-1x - 2))^2 - 4((-3x - 2)/(-1x - 2)) - 4) - 1| - 3) - 2) + 1 and g(x) = -3e^(-2((-3((-1x - 3)/(1x + 1)) + 1)/(3((-1x - 3)/(1x + 1))))) - 1 from x = -3.0 to x = -2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_3_3_150
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-1(5(2cos(2π(-1|x - 3|) - 2) + 2) - 4))/(2(5(2cos(2π(-1|x - 3|) - 2) + 2) - 4) + 1), g(x) = -1e^(-1(2(4x + 1)^2 + 4(4x + 1) - 5)) - 2, x = 3.0, and x = 3.1. 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_3_3_151
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -3|(3e^(-2(1|(-3x - 1) - 3| + 3)))| - 1 and g(x) = -2cos(3π(-4((-1x + 1)/(-1x - 1)) - 4) + 3) from x = -1.2 to x = -1.0999999999999999. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_3_3_152
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -3sin(2π(-3|(-2|(-1x^2 - 1x + 5) + 3| - 2) + 1|) + 3) + 2 and g(x) = 1(-5((2x - 1)/(-2x + 3)) - 4) from x = 4.7 to x = 4.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_3_3_153
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 1|((3(4(-1sin(3πx) - 1) + 1) - 3)/(1(4(-1sin(3πx) - 1) + 1) + 3)) + 2| - 3 and g(x) = (-3(2(-3cos(1πx) - 2)) + 3)/(2(2(-3cos(1πx) - 2))) between the vertical lines x = -1.6 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_3_3_154
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -3(2|((-2(2cos(3πx - 3) - 3) + 2)/(-2(2cos(3πx - 3) - 3))) - 1| + 3) + 4, g(x) = -1(4(-2|x + 2| + 2)^2 - 5(-2|x + 2| + 2))^2 - 1(4(-2|x + 2| + 2)^2 - 5(-2|x + 2| + 2)) - 1, x = -1.8, and x = -0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
6.0
|
math
|
train
|
math_algebra_func_area_level_3_3_155
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 3|((2(3(-3cos(2πx + 3) - 2)^2 - 1(-3cos(2πx + 3) - 2) - 1) - 1)/(-1(3(-3cos(2πx + 3) - 2)^2 - 1(-3cos(2πx + 3) - 2) - 1) + 3))| + 2 and g(x) = 1|(3sin(2π(-5x^2 - 5x - 3) + 3) + 3) - 3| + 2 from x = 2.1 to x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_3_3_156
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 2|(4(5((-2x + 1)/(-1x + 2))^2 + 1((-2x + 1)/(-1x + 2)) - 5)^2 + 1(5((-2x + 1)/(-1x + 2))^2 + 1((-2x + 1)/(-1x + 2)) - 5) - 3)| + 2 and g(x) = 2|(3cos(1π(-1|x + 3| + 2) + 1) - 3) - 1| + 3 between the vertical lines x = -0.4 and x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
129.4
|
math
|
train
|
math_algebra_func_area_level_3_3_157
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-3(5((-3(3e^(-1x) - 1) - 2)/(2(3e^(-1x) - 1) - 3))^2 + 4((-3(3e^(-1x) - 1) - 2)/(2(3e^(-1x) - 1) - 3)) - 4))/(1(5((-3(3e^(-1x) - 1) - 2)/(2(3e^(-1x) - 1) - 3))^2 + 4((-3(3e^(-1x) - 1) - 2)/(2(3e^(-1x) - 1) - 3)) - 4) - 3), g(x) = 1((3(-2sin(1πx - 3)) - 1)/(3(-2sin(1πx - 3)) - 2)) - 4, x = 2.8, and x = 4.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4.7
|
math
|
train
|
math_algebra_func_area_level_3_3_158
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-3(1cos(2π(1|(1|x| - 1) - 3| + 2)) - 3) - 2)/(3(1cos(2π(1|(1|x| - 1) - 3| + 2)) - 3) - 1), g(x) = -1|(-2|(-2x - 4) - 2| - 1) + 2| + 3, x = -4.2, and x = -1.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
5.0
|
math
|
train
|
math_algebra_func_area_level_3_3_159
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-3(-1(2(-2x - 5)^2 + 2(-2x - 5) - 5)^2 + 1(2(-2x - 5)^2 + 2(-2x - 5) - 5) - 4))/(-2(-1(2(-2x - 5)^2 + 2(-2x - 5) - 5)^2 + 1(2(-2x - 5)^2 + 2(-2x - 5) - 5) - 4) + 1) and g(x) = 4(-1|(-2x^2 + 4x - 5) + 3| + 2) - 5 from x = 0.6 to x = 1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.9
|
math
|
train
|
math_algebra_func_area_level_3_3_160
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 3cos(2π(1|(-2|((-1x + 2)/(-3x - 3)) - 3| + 3) + 1| - 1)) - 3 and g(x) = (3(2(1x - 1) + 2) + 2)/(-3(2(1x - 1) + 2) + 4) between the vertical lines x = -1.1 and x = -1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_3_3_161
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (1((-1(-4(-2|x - 1|) - 3) + 3)/(-2(-4(-2|x - 1|) - 3) + 3)) + 3)/(2((-1(-4(-2|x - 1|) - 3) + 3)/(-2(-4(-2|x - 1|) - 3) + 3)) + 2) and g(x) = (-3(-1e^(1((1x)/(2x))) - 2) - 1)/(3(-1e^(1((1x)/(2x))) - 2) - 1) from x = 0.4 to x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.1
|
math
|
train
|
math_algebra_func_area_level_3_3_162
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (2(-1|((-3(1x - 2) - 1)/(-1(1x - 2) + 2)) - 3| + 1) - 3)/(-2(-1|((-3(1x - 2) - 1)/(-1(1x - 2) + 2)) - 3| + 1)) and g(x) = 2e^(1(-1(-5x^2 + 2x - 3) - 5)) - 3 from x = 0.2 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.0
|
math
|
train
|
math_algebra_func_area_level_3_3_163
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1((1(-5(2sin(3πx - 1) + 2)^2 - 4(2sin(3πx - 1) + 2) - 3) + 2)/(1(-5(2sin(3πx - 1) + 2)^2 - 4(2sin(3πx - 1) + 2) - 3))) - 2 and g(x) = 1(-2cos(1π((-2x - 2)/(-1x)) + 2))^2 - 5 from x = -0.2 to 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_3_3_164
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-1((-1(-1sin(2π((-1x + 2)/(2x + 1)) + 2) - 1))/(1(-1sin(2π((-1x + 2)/(2x + 1)) + 2) - 1))) - 1)/(-2((-1(-1sin(2π((-1x + 2)/(2x + 1)) + 2) - 1))/(1(-1sin(2π((-1x + 2)/(2x + 1)) + 2) - 1))) - 3) and g(x) = -5(1((2x + 1)/(3x + 3)) - 4)^2 + 2(1((2x + 1)/(3x + 3)) - 4) + 5 from x = -1.1 to x = -1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
-174.6
|
math
|
train
|
math_algebra_func_area_level_3_3_165
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 3(-1((-2((-3x + 1)/(-3x + 4)) + 3)/(-2((-3x + 1)/(-3x + 4)) + 1))^2 - 2((-2((-3x + 1)/(-3x + 4)) + 3)/(-2((-3x + 1)/(-3x + 4)) + 1)) + 4)^2 - 3 and g(x) = (2(5(-3x + 1) - 5) + 3)/(-3(5(-3x + 1) - 5) - 3) from x = -2.6 to x = -2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.5
|
math
|
train
|
math_algebra_func_area_level_3_3_166
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -2sin(1π(-5(-4((1x - 3)/(-2x - 2)) + 2)^2 + 3(-4((1x - 3)/(-2x - 2)) + 2) + 2) - 1) and g(x) = 5(-1|(3|x - 3| + 1) - 3| + 1) + 2 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}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_3_3_167
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3(-2|(3cos(3π(-3x - 3) + 2) - 2) - 1| + 2) - 2, g(x) = 1(-4(-1x + 5)^2 + 4(-1x + 5) + 2)^2 + 1(-4(-1x + 5)^2 + 4(-1x + 5) + 2) + 1, x = 3.7, and x = 3.8. 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_3_3_168
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (3(3|((-1((-1x + 2)/(2x + 1)))/(2((-1x + 2)/(2x + 1)) + 3)) + 2| - 1) + 3)/(2(3|((-1((-1x + 2)/(2x + 1)))/(2((-1x + 2)/(2x + 1)) + 3)) + 2| - 1) - 1) and g(x) = -2|(4(1x + 2) + 5) - 1| + 2 between the vertical lines x = -1.4 and x = -1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
8.1
|
math
|
train
|
math_algebra_func_area_level_3_3_169
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-2(3((-1(-3|x| + 3))/(2(-3|x| + 3)))^2 - 3((-1(-3|x| + 3))/(2(-3|x| + 3))) - 4) + 1)/(-1(3((-1(-3|x| + 3))/(2(-3|x| + 3)))^2 - 3((-1(-3|x| + 3))/(2(-3|x| + 3))) - 4) - 1), g(x) = 3(-3cos(1π((-2x - 2)/(-3x + 1))) + 2) + 4, x = -0.0, and x = 0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.6
|
math
|
train
|
math_algebra_func_area_level_3_3_170
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -2sin(2π(4(-3|(2x^2 - 3x - 1) + 1| - 1) + 5) - 2) + 1, g(x) = (-2(-1(2|x + 3| - 3) + 3))/(2(-1(2|x + 3| - 3) + 3) + 2), x = -1.9, and x = -1.7999999999999998. 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_3_3_171
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-1(3((-1((3x + 2)/(-2x + 1)) - 1)/(2((3x + 2)/(-2x + 1)) + 1))^2 - 4((-1((3x + 2)/(-2x + 1)) - 1)/(2((3x + 2)/(-2x + 1)) + 1)) - 5))/(2(3((-1((3x + 2)/(-2x + 1)) - 1)/(2((3x + 2)/(-2x + 1)) + 1))^2 - 4((-1((3x + 2)/(-2x + 1)) - 1)/(2((3x + 2)/(-2x + 1)) + 1)) - 5) + 1), g(x) = -1(3|(-2x - 3) - 1| - 2) + 3, x = -2.9, and x = -1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4.9
|
math
|
train
|
math_algebra_func_area_level_3_3_172
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -5(-3|(2(2x + 5) - 4)| + 3) - 1 and g(x) = -2|((-1((-1x + 3)/(-3x - 3)) + 3)/(1((-1x + 3)/(-3x - 3)))) - 3| from x = -1.7 to x = -1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.7
|
math
|
train
|
math_algebra_func_area_level_3_3_173
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 4((1(-3sin(3π(5x^2 + 1x + 3) - 1) - 3) + 3)/(-1(-3sin(3π(5x^2 + 1x + 3) - 1) - 3) - 3)) and g(x) = -5(1(-5x^2 + 4) + 1)^2 - 4(1(-5x^2 + 4) + 1) + 3 between the vertical lines x = -0.9 and x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
146.7
|
math
|
train
|
math_algebra_func_area_level_3_3_174
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -2((3(-5((-2x)/(-1x - 2)) - 1) + 2)/(-1(-5((-2x)/(-1x - 2)) - 1) - 3))^2 + 3((3(-5((-2x)/(-1x - 2)) - 1) + 2)/(-1(-5((-2x)/(-1x - 2)) - 1) - 3)) - 1, g(x) = -1|(-1|(-3|x - 1| - 1) + 1| + 2) - 3| + 2, x = -0.1, 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_3_3_175
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -4((-1((-3(2|x + 3|))/(-3(2|x + 3|) - 1)))/(-3((-3(2|x + 3|))/(-3(2|x + 3|) - 1)) + 1))^2 - 1((-1((-3(2|x + 3|))/(-3(2|x + 3|) - 1)))/(-3((-3(2|x + 3|))/(-3(2|x + 3|) - 1)) + 1)) + 4 and g(x) = (-2(-1(-3x^2 - 1x - 1) + 2) - 2)/(2(-1(-3x^2 - 1x - 1) + 2) - 1) between the vertical lines x = -3.2 and x = -3.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.5
|
math
|
train
|
math_algebra_func_area_level_3_3_176
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -2sin(1π(-3|(2(-2|x - 2| + 1)^2 + 4(-2|x - 2| + 1)) - 1| + 2) + 2) - 1, g(x) = (-3((1(1|x - 2| - 3) - 2)/(-1(1|x - 2| - 3) - 3)) + 1)/(-2((1(1|x - 2| - 3) - 2)/(-1(1|x - 2| - 3) - 3)) + 1), x = -2.7, and x = -2.6. 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_3_3_177
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1((-1(-3(-3cos(3πx) - 1) - 5) + 1)/(3(-3(-3cos(3πx) - 1) - 5) - 1))^2 + 5((-1(-3(-3cos(3πx) - 1) - 5) + 1)/(3(-3(-3cos(3πx) - 1) - 5) - 1)) and g(x) = -5(-1|(-2|x + 1| - 3) + 2| + 1)^2 - 4(-1|(-2|x + 1| - 3) + 2| + 1) + 4 from x = -1.2 to x = -1.0999999999999999. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.2
|
math
|
train
|
math_algebra_func_area_level_3_3_178
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -2(-3sin(3π((3((-2x + 1)/(3x + 1)) - 2)/(-3((-2x + 1)/(3x + 1)) + 1)) + 1) + 3)^2 - 5(-3sin(3π((3((-2x + 1)/(3x + 1)) - 2)/(-3((-2x + 1)/(3x + 1)) + 1)) + 1) + 3) + 2 and g(x) = -1cos(1π((1((1x)/(2x)) - 2)/(3((1x)/(2x)))) + 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}"
]
}
|
4.7
|
math
|
train
|
math_algebra_func_area_level_3_3_179
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -4(-1(5(-3x - 1) - 4) - 2) and g(x) = (-2(-4(-2e^(-1x))^2 + 3(-2e^(-1x))) + 3)/(1(-4(-2e^(-1x))^2 + 3(-2e^(-1x))) + 2) between the vertical lines x = -0.4 and x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
105.5
|
math
|
train
|
math_algebra_func_area_level_3_3_180
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (2(-1(-3(-2cos(3πx) - 3) + 2)))/(2(-1(-3(-2cos(3πx) - 3) + 2)) - 1), g(x) = -2|(-1(2|x + 2| - 3)^2 - 1(2|x + 2| - 3) + 3) - 3| + 3, x = -2.7, and x = -1.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
6.0
|
math
|
train
|
math_algebra_func_area_level_3_3_181
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 2sin(3π((-1(-5(3x^2 + 1x + 2) - 3) - 1)/(-3(-5(3x^2 + 1x + 2) - 3) - 2)) - 2) - 3, g(x) = -3|(-1((3x + 3)/(2x - 1)) - 4) + 3| + 1, x = -0.8, and x = -0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.6
|
math
|
train
|
math_algebra_func_area_level_3_3_182
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-3(-1e^(1(1(-2x^2 + 4x - 1)^2 + 3(-2x^2 + 4x - 1) - 5)) - 2) - 1)/(2(-1e^(1(1(-2x^2 + 4x - 1)^2 + 3(-2x^2 + 4x - 1) - 5)) - 2) + 1) and g(x) = (1((1(1x^2 - 4x - 2))/(-1(1x^2 - 4x - 2) + 2)) + 1)/(-2((1(1x^2 - 4x - 2))/(-1(1x^2 - 4x - 2) + 2))) from x = -0.6 to x = 4.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
12.4
|
math
|
train
|
math_algebra_func_area_level_3_3_183
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1((-3((3((2x)/(1x + 1)) + 2)/(2((2x)/(1x + 1)) - 3)))/(2((3((2x)/(1x + 1)) + 2)/(2((2x)/(1x + 1)) - 3)) - 3)) - 3 and g(x) = (1(2sin(1π((-2x - 2)/(-2x - 3)) + 2) + 3))/(-2(2sin(1π((-2x - 2)/(-2x - 3)) + 2) + 3) + 3) from x = -1.2 to x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
62.3
|
math
|
train
|
math_algebra_func_area_level_3_3_184
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -2cos(2π((-1(1|(5x - 1) + 1| + 1) + 1)/(2(1|(5x - 1) + 1| + 1) - 1)) + 1) + 2, g(x) = -3((2(1e^(2x) - 1) - 2)/(-1(1e^(2x) - 1) + 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}"
]
}
|
0.0
|
math
|
train
|
math_algebra_func_area_level_3_3_185
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 3|((-2((-2(-5x - 2) - 3)/(3(-5x - 2) + 1)) - 2)/(-2((-2(-5x - 2) - 3)/(3(-5x - 2) + 1)))) + 3| - 1 and g(x) = 3sin(1π(1(1x^2 + 5x + 2) + 3) - 2) + 1 from x = -0.0 to x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_3_3_186
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1((1(-2|((1x - 2)/(2x - 3))| - 1) - 2)/(-3(-2|((1x - 2)/(2x - 3))| - 1) + 1))^2 - 4 and g(x) = (2(5(4x^2 - 1x - 5) - 1))/(-2(5(4x^2 - 1x - 5) - 1) + 3) from x = -1.1 to x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
8.3
|
math
|
train
|
math_algebra_func_area_level_3_3_187
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -3(-2(-3|(-3e^(-1x)) + 1| + 1)^2 + 3(-3|(-3e^(-1x)) + 1| + 1) + 1) + 5, g(x) = 2((3(-3cos(2πx) + 1) + 2)/(-3(-3cos(2πx) + 1) + 1)) - 4, x = 1.2, and x = 1.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
6.5
|
math
|
train
|
math_algebra_func_area_level_3_3_188
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -1e^(1((3(-3|(4x + 5) - 3| - 2) - 3)/(-2(-3|(4x + 5) - 3| - 2) + 3))) - 3 and g(x) = -1(-2cos(2π(2|x - 3| + 2) - 3))^2 - 3(-2cos(2π(2|x - 3| + 2) - 3)) - 1 between the vertical lines x = -2.9 and x = -2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.1
|
math
|
train
|
math_algebra_func_area_level_3_3_189
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -1|(-1(1(1sin(3πx + 2))^2 + 2(1sin(3πx + 2)) - 2)^2 + 4)| + 2, g(x) = 1((-3(-2x + 3))/(1(-2x + 3) + 1)) + 4, x = -4.9, and x = -4.6. 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_3_3_190
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 2(-3(3cos(1π(-2|x - 2| - 1) - 3) - 1)) + 1, g(x) = -2cos(1π(-1|(-2|x + 2| - 1) + 3| - 2)) - 3, x = -1.2, and x = -0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.2
|
math
|
train
|
math_algebra_func_area_level_3_3_191
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1|(2cos(2π(-1|(-1|x| - 2) + 1|) - 3) - 1) + 2| and g(x) = -2cos(2π(1((2x + 2)/(-3x + 2)) - 5) - 2) + 1 from x = 1.2 to x = 1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.7
|
math
|
train
|
math_algebra_func_area_level_3_3_192
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 4(1((1((3x + 3)/(2x + 3)) + 1)/(-2((3x + 3)/(2x + 3)) - 3))^2 - 5((1((3x + 3)/(2x + 3)) + 1)/(-2((3x + 3)/(2x + 3)) - 3)) - 3) + 5, g(x) = 5(-3cos(1π(1x^2 + 1x + 1) + 2) - 1) - 4, x = 1.9, and x = 2.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4.5
|
math
|
train
|
math_algebra_func_area_level_3_3_193
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -2sin(2π(1|(4((-2x - 3)/(1x))^2 + 2((-2x - 3)/(1x)) + 4) - 1|) - 1) - 1 and g(x) = -3|((-2((2x - 2)/(1x + 2)) + 2)/(1((2x - 2)/(1x + 2)))) - 2| + 3 between the vertical lines x = 1.7 and 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_3_3_194
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 3cos(3π(3|(1|(-2x^2 - 2x - 4) + 1| - 2) + 2| + 3)) + 1 and g(x) = 2|(-1(1x + 4)^2) + 3| + 2 between the vertical lines x = -2.2 and x = -2.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_3_3_195
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (3(-1((-2(2x^2 - 1x + 2) + 3)/(-2(2x^2 - 1x + 2)))^2 - 5((-2(2x^2 - 1x + 2) + 3)/(-2(2x^2 - 1x + 2))) + 3) - 1)/(3(-1((-2(2x^2 - 1x + 2) + 3)/(-2(2x^2 - 1x + 2)))^2 - 5((-2(2x^2 - 1x + 2) + 3)/(-2(2x^2 - 1x + 2))) + 3)), g(x) = 2e^(-2(1(1|x - 2|)^2 + 1(1|x - 2|) - 2)) + 1, x = 1.1, and x = 3.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
70.3
|
math
|
train
|
math_algebra_func_area_level_3_3_196
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 5(-3e^(2((1(4x^2 - 2x - 3) + 2)/(-2(4x^2 - 2x - 3) - 1))) + 3) + 1 and g(x) = -1(-2(2sin(1πx - 2))^2 - 3)^2 - 4(-2(2sin(1πx - 2))^2 - 3) - 5 between the vertical lines x = -0.4 and x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
44.2
|
math
|
train
|
math_algebra_func_area_level_3_3_197
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 2((-1(-2(2x + 2)^2 - 1(2x + 2)) + 2)/(1(-2(2x + 2)^2 - 1(2x + 2)) + 3))^2 - 1((-1(-2(2x + 2)^2 - 1(2x + 2)) + 2)/(1(-2(2x + 2)^2 - 1(2x + 2)) + 3)) + 4 and g(x) = 1|((-1((3x - 2)/(-2x + 1)) - 3)/(-2((3x - 2)/(-2x + 1)) - 1)) + 1| + 2 from x = 0.7 to x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
14.0
|
math
|
train
|
math_algebra_func_area_level_3_3_198
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (3(3(-3e^(-1(-1x^2 + 1x + 5)) - 1)^2 + 3(-3e^(-1(-1x^2 + 1x + 5)) - 1) + 3) - 3)/(3(3(-3e^(-1(-1x^2 + 1x + 5)) - 1)^2 + 3(-3e^(-1(-1x^2 + 1x + 5)) - 1) + 3) - 2), g(x) = 3|(-3(-2x - 1) + 5) + 2| - 2, x = -1.8, and x = -1.5. 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_3_3_199
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-2(1(-3(2cos(2πx - 3) + 3)^2 + 2(2cos(2πx - 3) + 3) - 5) + 2) - 2)/(-3(1(-3(2cos(2πx - 3) + 3)^2 + 2(2cos(2πx - 3) + 3) - 5) + 2) + 4), g(x) = 1|(5(-4x^2 + 2x) + 5) - 3| - 2, x = -0.3, and x = 0.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.4
|
math
|
train
|
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