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_800
|
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((3x)/(2x + 2))^2 + 5((3x)/(2x + 2)) + 3) - 1| + 3)^2 - 5(-1|(2((3x)/(2x + 2))^2 + 5((3x)/(2x + 2)) + 3) - 1| + 3) - 4, g(x) = -2sin(1π(-3(5x)^2 + 5(5x) + 4) + 1) - 2, x = -0.4, and x = -0.30000000000000004. 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_801
|
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(-3sin(2πx - 1) + 3) - 5)^2 + 5(3(-3sin(2πx - 1) + 3) - 5) - 2) + 2| - 1, g(x) = (3(-5(1|x + 1|) - 1) - 3)/(2(-5(1|x + 1|) - 1) - 1), x = -0.6, and x = -0.5. 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_802
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -3(4(-2((-2x)/(1x - 2))^2 + 5((-2x)/(1x - 2)) + 4)^2 + 2(-2((-2x)/(1x - 2))^2 + 5((-2x)/(1x - 2)) + 4) - 5) - 4 and g(x) = (2(4(-3|x - 2|)^2 - 5(-3|x - 2|) - 1) - 3)/(-3(4(-3|x - 2|)^2 - 5(-3|x - 2|) - 1) - 2) from x = 1.2 to x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
5.6
|
math
|
train
|
math_algebra_func_area_level_3_3_803
|
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(-3|x + 1| + 1) - 4) + 1)/(-3(-1(-3|x + 1| + 1) - 4))) - 3|, g(x) = 3sin(2π((-3(2x + 4) + 3)/(-3(2x + 4) - 3)) + 1) - 1, x = -2.6, and x = -2.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_3_3_804
|
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(-1|(1((-2x + 3)/(1x - 3)) + 4) + 2| + 3) - 3 and g(x) = 2cos(1π(1|(-4x + 3) - 3| + 3)) between the vertical lines x = -3.7 and x = -3.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.7
|
math
|
train
|
math_algebra_func_area_level_3_3_805
|
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(-2|((1(3|x + 1| + 3) + 3)/(1(3|x + 1| + 3) + 3))|) + 2 and g(x) = 3((3(-3sin(3πx - 2) + 2) + 3)/(-2(-3sin(3πx - 2) + 2)))^2 - 2((3(-3sin(3πx - 2) + 2) + 3)/(-2(-3sin(3πx - 2) + 2))) + 1 between the vertical lines x = 4.3 and x = 4.4. 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_806
|
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(1cos(2πx) + 2) - 5) - 3)/(1(3(1cos(2πx) + 2) - 5)))^2 - 5((1(3(1cos(2πx) + 2) - 5) - 3)/(1(3(1cos(2πx) + 2) - 5))) - 5 and g(x) = 2sin(1π(-2|(-1|x + 3| + 1) - 2|) - 1) between the vertical lines x = -4.8 and x = -4.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4.0
|
math
|
train
|
math_algebra_func_area_level_3_3_807
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 3e^(1(-4(-1|(2x - 4) + 2| + 2) - 2)) - 1 and g(x) = 2|(4(3|x - 1| - 2) - 3) + 2| + 2 between the vertical lines x = -0.5 and x = 2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
30.5
|
math
|
train
|
math_algebra_func_area_level_3_3_808
|
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|(1|(-5(4x + 3) + 4) - 1| + 2) + 1| - 3 and g(x) = -2|(3sin(2π(2x^2 - 3x - 1) - 1) + 3) + 2| between the vertical lines x = -0.6 and x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.5
|
math
|
train
|
math_algebra_func_area_level_3_3_809
|
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|(-1(1|(1x - 5)| - 2) + 4) + 1| - 3 and g(x) = 5(1|(-2sin(3πx - 1) + 3) - 3| - 2)^2 + 4(1|(-2sin(3πx - 1) + 3) - 3| - 2) + 1 between the vertical lines x = 0.8 and x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.3
|
math
|
train
|
math_algebra_func_area_level_3_3_810
|
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(-1e^(-1(2|(1|x + 2| + 1) - 1| + 2)) - 2)^2 - 1(-1e^(-1(2|(1|x + 2| + 1) - 1| + 2)) - 2) and g(x) = (1((3(4x^2 + 5x - 4) + 1)/(2(4x^2 + 5x - 4) + 2)) - 3)/(-1((3(4x^2 + 5x - 4) + 1)/(2(4x^2 + 5x - 4) + 2)) - 1) between the vertical lines x = -1.7 and x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
30.7
|
math
|
train
|
math_algebra_func_area_level_3_3_811
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (1((-2(-3sin(1π(2|x| - 1) - 2) + 1) + 3)/(-2(-3sin(1π(2|x| - 1) - 2) + 1))) + 3)/(-2((-2(-3sin(1π(2|x| - 1) - 2) + 1) + 3)/(-2(-3sin(1π(2|x| - 1) - 2) + 1)))) and g(x) = -2cos(1π((2((-1x - 2)/(-2x)) - 3)/(-1((-1x - 2)/(-2x))))) + 2 from x = -2.3 to x = -1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.5
|
math
|
train
|
math_algebra_func_area_level_3_3_812
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -5(3cos(3π(2(-3x - 4) + 3) - 1) + 3)^2 + 5(3cos(3π(2(-3x - 4) + 3) - 1) + 3) + 5 and g(x) = -5(2|(-3x + 4) + 2| + 3)^2 - 1(2|(-3x + 4) + 2| + 3) - 4 from x = 2.1 to x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
5.7
|
math
|
train
|
math_algebra_func_area_level_3_3_813
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-2(-1e^(1(1(4x^2 + 2x - 3) + 2))) + 1)/(-1(-1e^(1(1(4x^2 + 2x - 3) + 2))) - 3), g(x) = -2(1|(2|x - 3| - 3) + 1|) + 1, x = -1.0, and x = 0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
9.7
|
math
|
train
|
math_algebra_func_area_level_3_3_814
|
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(-3x^2 + 5) - 2) + 1))/(-1(2(-1(-3x^2 + 5) - 2) + 1) + 2), g(x) = (-1(-1(2x^2 - 4x + 1) + 5) + 1)/(3(-1(2x^2 - 4x + 1) + 5) - 1), x = -0.7, and x = 1.5. Round your answer 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_815
|
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(4x - 5)^2 - 3(4x - 5) + 4) - 4) - 3) - 1, g(x) = (-1(-5(-3x^2 + 4x + 4)^2) - 2)/(-2(-5(-3x^2 + 4x + 4)^2)), x = 0.9, and x = 1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_3_3_816
|
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((3(-5(-4x + 1)^2 + 1(-4x + 1) + 5) + 3)/(-1(-5(-4x + 1)^2 + 1(-4x + 1) + 5) + 2)) - 1) + 3, g(x) = -2(2sin(3π(-1x - 4) + 2) - 2)^2 - 1(2sin(3π(-1x - 4) + 2) - 2) + 5, x = 1.9, and x = 2.2. Round your answer 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_817
|
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((-2(1cos(3π(1|x| - 2) + 2)) - 1)/(3(1cos(3π(1|x| - 2) + 2)) - 2))^2 - 3((-2(1cos(3π(1|x| - 2) + 2)) - 1)/(3(1cos(3π(1|x| - 2) + 2)) - 2)) - 2 and g(x) = -1(2(-3|x + 2| - 3) + 5)^2 - 1(2(-3|x + 2| - 3) + 5) between the vertical lines x = -2.1 and x = -1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.7
|
math
|
train
|
math_algebra_func_area_level_3_3_818
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 5(-4(-2sin(1π((1x - 3)/(-3x - 2)) + 2) - 1)^2 - 5(-2sin(1π((1x - 3)/(-3x - 2)) + 2) - 1) - 2)^2 + 2(-4(-2sin(1π((1x - 3)/(-3x - 2)) + 2) - 1)^2 - 5(-2sin(1π((1x - 3)/(-3x - 2)) + 2) - 1) - 2) - 3, g(x) = -3sin(1π((3(-3x^2 + 4x) + 3)/(1(-3x^2 + 4x)))) - 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}"
]
}
|
5.5
|
math
|
train
|
math_algebra_func_area_level_3_3_819
|
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|(1(-2cos(2π(-2x^2 - 5x - 3) - 3))^2 + 1(-2cos(2π(-2x^2 - 5x - 3) - 3)) + 1) - 1| + 1 and g(x) = -1sin(2π((-3(-1x^2 + 1x - 3) + 3)/(-2(-1x^2 + 1x - 3) - 2)) + 1) + 2 between the vertical lines x = 1.5 and x = 1.6. 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_820
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 2((2(2|(1cos(2πx - 1)) - 1| - 1) - 1)/(2(2|(1cos(2πx - 1)) - 1| - 1)))^2 - 5((2(2|(1cos(2πx - 1)) - 1| - 1) - 1)/(2(2|(1cos(2πx - 1)) - 1| - 1))) and g(x) = (1(2(3e^(-2x))^2 + 4(3e^(-2x)) + 4) + 3)/(-1(2(3e^(-2x))^2 + 4(3e^(-2x)) + 4) - 3) from x = -3.6 to x = -3.1. 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_821
|
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(-3x + 2) - 1)/(2(-3x + 2) - 3))^2 + 3((-1(-3x + 2) - 1)/(2(-3x + 2) - 3)) + 2) + 4, g(x) = -1((2(-1x - 3) + 1)/(-1(-1x - 3) - 1)) + 3, x = -0.7, and x = 0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4.6
|
math
|
train
|
math_algebra_func_area_level_3_3_822
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -3((2(-2cos(2π(1x^2 + 4x) + 3) + 2) + 1)/(2(-2cos(2π(1x^2 + 4x) + 3) + 2) - 1)) - 3 and g(x) = (1(4(-4x^2 - 3x - 5)^2 - 5(-4x^2 - 3x - 5) - 4) - 3)/(1(4(-4x^2 - 3x - 5)^2 - 5(-4x^2 - 3x - 5) - 4) + 3) from x = 3.4 to x = 3.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.5
|
math
|
train
|
math_algebra_func_area_level_3_3_823
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1((-2(1|((3x + 2)/(-1x + 2)) - 3| + 1) - 1)/(2(1|((3x + 2)/(-1x + 2)) - 3| + 1) - 1))^2 - 3((-2(1|((3x + 2)/(-1x + 2)) - 3| + 1) - 1)/(2(1|((3x + 2)/(-1x + 2)) - 3| + 1) - 1)) - 4 and g(x) = (-2(-1e^(-2(-5x^2 + 5x + 3)) + 1) + 1)/(2(-1e^(-2(-5x^2 + 5x + 3)) + 1)) from x = -0.4 to x = 1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
6.7
|
math
|
train
|
math_algebra_func_area_level_3_3_824
|
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|(4x - 1) + 2| + 3)^2 - 3(-3|(4x - 1) + 2| + 3) + 3) + 3 and g(x) = 2(-1(3cos(2πx + 1) + 3) + 2) - 5 between the vertical lines x = -0.7 and x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_3_3_825
|
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(2|(1(4x - 4) - 2) + 1| + 1) - 2)/(1(2|(1(4x - 4) - 2) + 1| + 1)) and g(x) = 1|(4(2x)^2 + 3(2x) - 1) - 2| - 3 between the vertical lines x = -0.8 and x = -0.5. 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_826
|
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)/(1x + 3)) - 1| - 3)^2 - 1(3|((1x)/(1x + 3)) - 1| - 3) + 4))/(-3(1(3|((1x)/(1x + 3)) - 1| - 3)^2 - 1(3|((1x)/(1x + 3)) - 1| - 3) + 4) + 4), g(x) = 2cos(3π(-5(4x + 4) - 5) - 2) + 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}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_3_3_827
|
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(-1|((-1x + 1)/(-3x - 2)) - 3| - 2)^2 - 4(-1|((-1x + 1)/(-3x - 2)) - 3| - 2) + 5) - 3| - 2, g(x) = -3|(-1(3x)^2 + 1(3x) - 3) + 3|, x = -1.1, and x = -0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.9
|
math
|
train
|
math_algebra_func_area_level_3_3_828
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -4((-1(2(1cos(1πx + 1) - 2) + 2) + 2)/(3(2(1cos(1πx + 1) - 2) + 2)))^2 - 1 and g(x) = 3(3sin(1π(-3x) + 2) - 2) + 5 from x = -1.5 to x = -1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.3
|
math
|
train
|
math_algebra_func_area_level_3_3_829
|
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(1|(3sin(2π(-3x - 2) - 2) - 3) + 3| + 1) and g(x) = 1cos(3π(-3(1x - 2) - 2) + 1) + 2 between the vertical lines x = 2.0 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_830
|
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 - 3)/(-2x - 1)) - 1)/(1((3x - 3)/(-2x - 1)) + 3)) + 2|) - 2)/(-1(-3|((-1((3x - 3)/(-2x - 1)) - 1)/(1((3x - 3)/(-2x - 1)) + 3)) + 2|) + 2), g(x) = 2(-1(2x - 3)^2 + 1(2x - 3) + 1) + 1, x = 1.1, and x = 2.4. 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_3_3_831
|
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|((3((1x + 2)/(-2x - 1)) - 1)/(3((1x + 2)/(-2x - 1)) - 1)) - 3| - 2) - 3, g(x) = 1|(4(-1cos(1πx - 1) - 1) + 2) + 3|, x = -1.7, and x = -1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.8
|
math
|
train
|
math_algebra_func_area_level_3_3_832
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -2((3((-2(-3|x - 2| + 2) - 1)/(3(-3|x - 2| + 2) + 3)) + 1)/(1((-2(-3|x - 2| + 2) - 1)/(3(-3|x - 2| + 2) + 3)))) - 4 and g(x) = -1cos(1π(-2(1x)^2 + 4(1x) + 4) - 3) - 3 from x = 1.3 to x = 2.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.7
|
math
|
train
|
math_algebra_func_area_level_3_3_833
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 1cos(2π((3(2|(-5x + 5) + 1| - 2) + 2)/(-2(2|(-5x + 5) + 1| - 2) + 3)) + 3) + 1 and g(x) = -1(-1e^(-1((-1x + 1)/(2x + 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}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_3_3_834
|
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|(-3|(-1x - 3) - 1| + 2)| - 3)^2 + 5(-2|(-3|(-1x - 3) - 1| + 2)| - 3) + 5, g(x) = -2|(-3|(3sin(2πx - 1) + 3) - 1|) - 2| + 1, x = -4.7, and x = -4.6. 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_3_3_835
|
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((3(1sin(1πx) + 1) + 2)/(-2(1sin(1πx) + 1) - 2)) + 4) - 5 and g(x) = -3|(3sin(1π(3|x + 2| - 3) + 2)) - 1| between the vertical lines x = -4.1 and x = -3.8. 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_836
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 4((-1(2(3x + 2) - 2) + 2)/(-3(2(3x + 2) - 2)))^2 - 3((-1(2(3x + 2) - 2) + 2)/(-3(2(3x + 2) - 2))) + 2 and g(x) = 1(-5((1x)/(-3x - 3)) - 5)^2 + 5(-5((1x)/(-3x - 3)) - 5) + 4 from x = -0.2 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.9
|
math
|
train
|
math_algebra_func_area_level_3_3_837
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3cos(1π(-3(-2|(-5x^2 - 3x - 3) - 2| - 3)^2 + 1(-2|(-5x^2 - 3x - 3) - 2| - 3) + 3) + 3) + 1, g(x) = 1cos(1π(-4(-4x^2 - 4x + 3) + 1) + 3) - 1, x = -2.6, and x = -2.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_3_3_838
|
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(-1(-4(3|x + 3| - 3)^2 - 1(3|x + 3| - 3) + 4)^2 - 4(-4(3|x + 3| - 3)^2 - 1(3|x + 3| - 3) + 4) - 4) + 3)/(3(-1(-4(3|x + 3| - 3)^2 - 1(3|x + 3| - 3) + 4)^2 - 4(-4(3|x + 3| - 3)^2 - 1(3|x + 3| - 3) + 4) - 4)) and g(x) = -3(-3sin(3π(2|x + 2| - 1)) - 1) + 4 between the vertical lines x = -1.5 and x = -1.3. 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_839
|
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|(-1(4x^2 - 5x - 5) + 4) + 3| + 2) + 1 and g(x) = (-2(-3(3|x - 3|) + 4) + 2)/(-2(-3(3|x - 3|) + 4) + 3) between the vertical lines x = 2.6 and x = 2.7. 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_840
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (3(4((-2(-1|x - 3| + 2))/(-1(-1|x - 3| + 2) + 3))^2 - 1) - 1)/(2(4((-2(-1|x - 3| + 2))/(-1(-1|x - 3| + 2) + 3))^2 - 1) + 1), g(x) = 2|((2(1x) + 2)/(-3(1x) - 2)) - 3| + 2, x = 1.4, and x = 4.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
34.6
|
math
|
train
|
math_algebra_func_area_level_3_3_841
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -3|(2e^(1(3(-4x) + 2)) - 1) - 1| + 3, g(x) = 3cos(3π(-3|(5x) + 1|) + 1) + 3, x = 0.1, and x = 0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_3_3_842
|
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((-1(4(-3|x + 3| + 2) - 1) - 2)/(-3(4(-3|x + 3| + 2) - 1) - 3)) + 2 and g(x) = -1|(-1|(-5x^2 + 5x + 1)| + 1) + 2| between the vertical lines x = -3.7 and x = -2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
81.4
|
math
|
train
|
math_algebra_func_area_level_3_3_843
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -3e^(-2(-2((-2(1x - 2) + 3)/(2(1x - 2))) + 5)) - 1 and g(x) = 2(1sin(3π(1|x + 2| + 3) + 3) + 3)^2 - 4(1sin(3π(1|x + 2| + 3) + 3) + 3) - 1 from x = -3.8 to x = -3.2. 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_844
|
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(-2cos(2π(3|(-5x^2 + 1x + 5) + 1| + 2) - 2) + 1) - 2)/(3(-2cos(2π(3|(-5x^2 + 1x + 5) + 1| + 2) - 2) + 1) + 2) and g(x) = -1|(3(2cos(3πx - 2) + 2)^2 + 4(2cos(3πx - 2) + 2)) - 3| - 3 between the vertical lines x = 1.3 and x = 1.4000000000000001. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.5
|
math
|
train
|
math_algebra_func_area_level_3_3_845
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1|(-5(3|(4x + 2) - 2| - 1)^2 + 1(3|(4x + 2) - 2| - 1) + 1) - 1| - 3 and g(x) = -1(-1|(3e^(1x) + 1) - 1| + 3) - 1 from x = -0.1 to x = -0.0. 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_846
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 3((-3(-1cos(3π((-2x + 2)/(-3x + 4)) + 1)) + 2)/(2(-1cos(3π((-2x + 2)/(-3x + 4)) + 1)) - 1))^2 - 1((-3(-1cos(3π((-2x + 2)/(-3x + 4)) + 1)) + 2)/(2(-1cos(3π((-2x + 2)/(-3x + 4)) + 1)) - 1)) + 5 and g(x) = 3|(2((3x - 2)/(-3x - 3))^2 + 5((3x - 2)/(-3x - 3)) - 1) + 1| + 3 from x = 1.6 to x = 1.7000000000000002. 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_847
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -2|(-1(3|(5x^2 - 1x + 1) - 3| + 2) + 3) + 3| and g(x) = -3sin(2π(1(-2x - 2) - 2)) + 2 from x = 0.9 to x = 1.0. 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_848
|
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(1(-1(-5x - 3) + 2)^2 + 1(-1(-5x - 3) + 2) + 1) + 1 and g(x) = 1((-3(-3x^2 + 1x - 4))/(1(-3x^2 + 1x - 4) + 1)) between the vertical lines x = -1.2 and x = -1.0. 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_849
|
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(-1sin(1πx + 2) + 2) - 4) + 2)/(-1(-1(-1sin(1πx + 2) + 2) - 4) - 3)) + 3)/(3((-2(-1(-1sin(1πx + 2) + 2) - 4) + 2)/(-1(-1(-1sin(1πx + 2) + 2) - 4) - 3)) - 1), g(x) = 1(1|(1e^(-1x) - 1) - 3| + 3)^2 - 5(1|(1e^(-1x) - 1) - 3| + 3) - 5, x = -1.9, and x = -0.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
12.8
|
math
|
train
|
math_algebra_func_area_level_3_3_850
|
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(-2sin(3π(-4((2x - 2)/(1x + 1)) + 4) + 2) + 1) + 5 and g(x) = 3cos(1π(3|(1|x - 1| + 1) + 2| + 1) + 1) + 1 between the vertical lines x = 0.6 and x = 0.7. 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_851
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (1(2(-3cos(3π((2x - 2)/(-3x - 2)) + 3) + 3) - 1) - 2)/(-3(2(-3cos(3π((2x - 2)/(-3x - 2)) + 3) + 3) - 1) - 2) and g(x) = -1(-3(5x + 1))^2 + 2(-3(5x + 1)) + 1 from x = -0.0 to x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.5
|
math
|
train
|
math_algebra_func_area_level_3_3_852
|
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((2((-3(-1x + 1) + 2)/(1(-1x + 1) + 1)) - 1)/(1((-3(-1x + 1) + 2)/(1(-1x + 1) + 1)) + 2))) + 2, g(x) = (-2(-4(3x - 3)^2 + 3(3x - 3) + 2) + 1)/(1(-4(3x - 3)^2 + 3(3x - 3) + 2) + 2), x = 0.9, and x = 1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.6
|
math
|
train
|
math_algebra_func_area_level_3_3_853
|
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(-1(-4(-2|x + 2| - 1) - 3) + 5) + 5 and g(x) = 3cos(2π(4((1x + 3)/(-1x + 2))^2 + 2((1x + 3)/(-1x + 2)) + 1) - 1) between the vertical lines x = -2.6 and x = -1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
12.1
|
math
|
train
|
math_algebra_func_area_level_3_3_854
|
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(-2cos(1π(3|x + 2| + 1))) + 2)/(2(-2cos(1π(3|x + 2| + 1))) - 1)) - 3| - 3 and g(x) = -3(-4(-2e^(2x))^2 - 4(-2e^(2x)) + 3)^2 - 5(-4(-2e^(2x))^2 - 4(-2e^(2x)) + 3) - 5 between the vertical lines x = -3.5 and x = -3.4. Round 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_855
|
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|(4(2sin(3πx + 2) + 1)^2 + 3(2sin(3πx + 2) + 1) - 1) + 3| - 3) + 2|, g(x) = -3|(-3(-5x) - 1) + 3| - 1, x = 3.2, and x = 3.4. 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_856
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -2(-3(-2sin(2π(2|x| - 3) + 2) - 1)^2 - 2(-2sin(2π(2|x| - 3) + 2) - 1) + 2) - 2 and g(x) = 3(2sin(2π(-1|x + 3| - 1) - 3) + 3) + 4 from x = 2.5 to x = 2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.6
|
math
|
train
|
math_algebra_func_area_level_3_3_857
|
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(3cos(3πx - 1) + 2) - 3)/(2(3cos(3πx - 1) + 2) + 3)) + 1)^2 + 5(3((1(3cos(3πx - 1) + 2) - 3)/(2(3cos(3πx - 1) + 2) + 3)) + 1) - 1, g(x) = -2|(-3((1x + 2)/(-2x + 3)) - 5) - 2| + 1, x = 2.4, and x = 2.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
19.3
|
math
|
train
|
math_algebra_func_area_level_3_3_858
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 3((-1(-2|(-3|x - 2| + 2)| - 1) + 2)/(3(-2|(-3|x - 2| + 2)| - 1))) and g(x) = -3(-2(1x)^2 - 5(1x) + 4) - 1 from x = -3.1 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
53.2
|
math
|
train
|
math_algebra_func_area_level_3_3_859
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 1sin(1π(-2|((-1((-2x - 2)/(-1x)) - 3)/(-1((-2x - 2)/(-1x)) - 3)) + 2|) + 2) + 3, g(x) = 5(3|(4x - 1) + 1| - 1)^2 + 5(3|(4x - 1) + 1| - 1) + 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}"
]
}
|
0.5
|
math
|
train
|
math_algebra_func_area_level_3_3_860
|
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(-2|(4x^2 + 2x + 4) - 2| + 3) + 3)/(3(-2|(4x^2 + 2x + 4) - 2| + 3) + 2)) + 3)/(3((3(-2|(4x^2 + 2x + 4) - 2| + 3) + 3)/(3(-2|(4x^2 + 2x + 4) - 2| + 3) + 2)) + 1) and g(x) = 1|(2sin(3π(2|x + 2| + 1) + 1) - 2) - 2| + 3 between the vertical lines x = -0.5 and x = -0.0. Round 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_861
|
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(1π(-1|(-4(3x^2 + 1x + 3) + 1) + 2| + 2) - 1) - 3 and g(x) = -2|(-2(2x^2 + 3x + 2)^2 + 5(2x^2 + 3x + 2)) + 3| + 1 between the vertical lines x = 0.2 and x = 0.4. 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_862
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1|((2(-2cos(2π(-5x^2 - 2x - 2) + 1) + 2) - 2)/(1(-2cos(2π(-5x^2 - 2x - 2) + 1) + 2) - 3)) - 1| - 1 and g(x) = (1(-2(3e^(1x) - 3) - 3) - 1)/(-3(-2(3e^(1x) - 3) - 3)) from x = -3.2 to 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_863
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1|(5(4(1x + 5)^2 - 3(1x + 5) - 1)^2 - 5) + 3| + 3 and g(x) = 4((2((-1x + 1)/(3x)) - 2)/(-1((-1x + 1)/(3x)) + 2)) + 2 from x = -4.3 to x = -3.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.0
|
math
|
train
|
math_algebra_func_area_level_3_3_864
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 4(-3cos(2π((1(3|x + 1| + 1))/(-3(3|x + 1| + 1) + 2))) + 2)^2 + 4(-3cos(2π((1(3|x + 1| + 1))/(-3(3|x + 1| + 1) + 2))) + 2) + 5, g(x) = 1((-2(-3x - 3) + 2)/(1(-3x - 3) + 3))^2 + 5((-2(-3x - 3) + 2)/(1(-3x - 3) + 3)) - 4, x = -0.3, and x = 0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
-113.0
|
math
|
train
|
math_algebra_func_area_level_3_3_865
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 3sin(3π(2((3(-5x^2 - 3x + 2) - 1)/(2(-5x^2 - 3x + 2) - 3)) + 1)) + 3 and g(x) = -1|(-4(3x^2 - 5x) - 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}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_3_3_866
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-1(5(4((1x + 3)/(3x + 1)))^2 - 4(4((1x + 3)/(3x + 1))) + 2) - 2)/(-3(5(4((1x + 3)/(3x + 1)))^2 - 4(4((1x + 3)/(3x + 1))) + 2) - 2) and g(x) = -1(1(1cos(1πx) - 3) + 4)^2 - 5(1(1cos(1πx) - 3) + 4) + 1 from x = -1.2 to x = -0.8. 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_867
|
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(-1(3e^(1(4x^2 - 2x + 3)) - 1) + 2) + 1)/(3(-1(3e^(1(4x^2 - 2x + 3)) - 1) + 2) - 2) and g(x) = 2|((1((2x - 1)/(-1x + 2)) + 1)/(-2((2x - 1)/(-1x + 2)) - 1)) + 2| - 2 between the vertical lines x = 0.2 and x = 0.3. 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_868
|
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(-3cos(1π(3|(-1x^2 + 5x + 1) + 3| - 1) - 2) + 3) + 2)/(3(-3cos(1π(3|(-1x^2 + 5x + 1) + 3| - 1) - 2) + 3) + 2) and g(x) = 3cos(2π(1(1|x - 3|) - 5) - 3) - 1 between the vertical lines x = -4.6 and x = -4.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_3_3_869
|
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|((2(3x^2 + 5x - 5) + 1)/(2(3x^2 + 5x - 5) + 3)) - 1| + 2)^2 - 1(-1|((2(3x^2 + 5x - 5) + 1)/(2(3x^2 + 5x - 5) + 3)) - 1| + 2) + 3, g(x) = -1|(-2cos(3π(-1|x + 1|) + 2) + 1) + 1| - 3, x = -2.0, and x = 0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
13.9
|
math
|
train
|
math_algebra_func_area_level_3_3_870
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -1cos(2π(-5((-1((2x - 1)/(-1x - 2)) - 3)/(-3((2x - 1)/(-1x - 2)) + 1)) + 4) - 1) - 1, g(x) = -1(1e^(1((-1x - 3)/(-1x - 2))) - 2)^2 + 3(1e^(1((-1x - 3)/(-1x - 2))) - 2) - 1, x = -0.5, and x = -0.4. 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_871
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 5(-4(-1((2x - 1)/(-1x - 3))^2 + 4((2x - 1)/(-1x - 3)))^2 - 1(-1((2x - 1)/(-1x - 3))^2 + 4((2x - 1)/(-1x - 3))) + 4) and g(x) = (-3(1(3x^2 + 2x - 2) + 3) + 3)/(-1(1(3x^2 + 2x - 2) + 3) + 2) from x = 0.1 to x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
32.8
|
math
|
train
|
math_algebra_func_area_level_3_3_872
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1e^(-1((-1(-4(-2|x - 1| + 1)^2 + 1(-2|x - 1| + 1) + 3) + 1)/(-2(-4(-2|x - 1| + 1)^2 + 1(-2|x - 1| + 1) + 3) + 3))) + 2 and g(x) = -2|(1e^(1((-2x + 3)/(-1x + 2))) - 3) + 3| + 2 from x = 0.2 to x = 0.9. Round 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_873
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -2|(-5(-2|(-3x + 5) + 1| + 1)^2 - 1(-2|(-3x + 5) + 1| + 1) + 2) + 1| - 2, g(x) = (-3((-1(1x + 5) - 1)/(1(1x + 5) - 2)) + 3)/(3((-1(1x + 5) - 1)/(1(1x + 5) - 2)) + 3), x = 1.9, and x = 2.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_3_3_874
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -2(2(1cos(2π(-3x - 2) - 2) - 1)^2 + 4(1cos(2π(-3x - 2) - 2) - 1) + 4) + 3 and g(x) = (1(-1|(-1x - 3) + 3| + 2) + 3)/(1(-1|(-1x - 3) + 3| + 2) - 2) from x = 2.5 to x = 2.6. 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_875
|
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|(2|(3(1x^2 - 4x - 3) + 3) - 1| + 2)| - 2 and g(x) = -4(-4(1cos(2πx - 3) - 2) - 5) - 3 between the vertical lines x = -0.7 and x = -0.3. 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_876
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 2|(4((-2((-1x - 2)/(-2x - 2)) - 2)/(1((-1x - 2)/(-2x - 2)) + 3))^2 + 4((-2((-1x - 2)/(-2x - 2)) - 2)/(1((-1x - 2)/(-2x - 2)) + 3)) + 1) - 1| and g(x) = -5(-3((-2x - 3)/(-3x)) - 4) + 5 from x = -1.0 to x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
5.2
|
math
|
train
|
math_algebra_func_area_level_3_3_877
|
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(-4(3cos(2π((3x + 1)/(1x + 2)) + 2) - 2)^2 - 5(3cos(2π((3x + 1)/(1x + 2)) + 2) - 2))^2 + 2(-4(3cos(2π((3x + 1)/(1x + 2)) + 2) - 2)^2 - 5(3cos(2π((3x + 1)/(1x + 2)) + 2) - 2)) - 4 and g(x) = 3(1sin(3π(2|x - 3| - 2)) - 3)^2 + 5(1sin(3π(2|x - 3| - 2)) - 3) + 3 between the vertical lines x = -1.8 and x = -1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
132.8
|
math
|
train
|
math_algebra_func_area_level_3_3_878
|
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(-2(1x^2 + 5x + 1) - 4)^2 - 2(-2(1x^2 + 5x + 1) - 4) - 5)^2 + 4(1(-2(1x^2 + 5x + 1) - 4)^2 - 2(-2(1x^2 + 5x + 1) - 4) - 5) - 5 and g(x) = (3(-2|(2e^(2x) - 3) + 3| - 1))/(2(-2|(2e^(2x) - 3) + 3| - 1) - 1) between the vertical lines x = -4.4 and x = -3.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
41.1
|
math
|
train
|
math_algebra_func_area_level_3_3_879
|
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(2(4x^2 + 1x)^2 + 2(4x^2 + 1x)) - 2) + 2| - 1 and g(x) = -1(-5(-3sin(3πx) - 1) + 1)^2 - 4(-5(-3sin(3πx) - 1) + 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}"
]
}
|
1.2
|
math
|
train
|
math_algebra_func_area_level_3_3_880
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -2(1cos(1π(1|(-1|x + 1|) + 2| - 3) - 3)) - 3 and g(x) = -1(4(-2x^2 + 5x - 1) - 4)^2 - 4(4(-2x^2 + 5x - 1) - 4) - 5 from x = 2.1 to x = 2.2. 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_881
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-1(2|(-5(-4x^2 - 1x - 4) + 4) + 3| + 2) + 1)/(-2(2|(-5(-4x^2 - 1x - 4) + 4) + 3| + 2) + 1) and g(x) = (-3((3(-2sin(3πx + 1) - 1) - 3)/(-2(-2sin(3πx + 1) - 1) - 2)) + 3)/(2((3(-2sin(3πx + 1) - 1) - 3)/(-2(-2sin(3πx + 1) - 1) - 2)) + 3) from x = -2.3 to x = -2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.0
|
math
|
train
|
math_algebra_func_area_level_3_3_882
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-2(5(-2(-3|x + 2|) - 5) - 3) + 3)/(1(5(-2(-3|x + 2|) - 5) - 3) + 2), g(x) = -2|(4(-4x^2 + 5x - 3) + 5) + 3|, x = 0.2, and x = 0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_3_3_883
|
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^(1((1(-2x^2 - 3x - 2) - 3)/(-2(-2x^2 - 3x - 2)))) + 2)^2 - 1(-3e^(1((1(-2x^2 - 3x - 2) - 3)/(-2(-2x^2 - 3x - 2)))) + 2) - 4 and g(x) = -1(1(-2sin(1πx) + 3) - 4)^2 + 3 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_3_3_884
|
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(-1(-4(1x + 3)^2 - 4(1x + 3) + 1) - 1))/(1(-1(-4(1x + 3)^2 - 4(1x + 3) + 1) - 1) + 3) and g(x) = -4(1|(-3x + 5) + 3| + 3) - 5 between the vertical lines x = -3.6 and x = -3.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
-48.6
|
math
|
train
|
math_algebra_func_area_level_3_3_885
|
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(-1cos(3π(-4x + 3) - 3) - 3) - 4)^2 + 1(-5(-1cos(3π(-4x + 3) - 3) - 3) - 4) - 5, g(x) = 3((1(-2sin(2πx + 2) + 3))/(1(-2sin(2πx + 2) + 3) - 2)) + 4, x = -4.9, and x = -4.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
119.4
|
math
|
train
|
math_algebra_func_area_level_3_3_886
|
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|((-1(-2(3|x + 2| + 2)) + 3)/(-3(-2(3|x + 2| + 2))))| - 3 and g(x) = 2cos(3π(-2|(3x + 4)| + 1) + 1) - 1 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}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_3_3_887
|
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(-1(-2|x - 3| - 1) - 1)^2) + 3)/(-1(-5(-1(-2|x - 3| - 1) - 1)^2)) and g(x) = 5(1(-2x + 4) - 2)^2 + 1(1(-2x + 4) - 2) - 3 between the vertical lines x = 0.6 and x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.5
|
math
|
train
|
math_algebra_func_area_level_3_3_888
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1|((2(-1|(-4x^2 - 1x - 5)| - 1) - 3)/(-2(-1|(-4x^2 - 1x - 5)| - 1) + 3))| + 1 and g(x) = 5(4(4x)^2 - 5(4x) - 3) + 2 from x = -0.1 to x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
7.1
|
math
|
train
|
math_algebra_func_area_level_3_3_889
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-3(-3(-1((2x + 2)/(1x + 2)) + 5)^2 + 1(-1((2x + 2)/(1x + 2)) + 5) + 4) - 1)/(3(-3(-1((2x + 2)/(1x + 2)) + 5)^2 + 1(-1((2x + 2)/(1x + 2)) + 5) + 4) - 1) and g(x) = (-1(2|((2x + 2)/(-1x - 3)) + 2| - 1) + 3)/(-2(2|((2x + 2)/(-1x - 3)) + 2| - 1) + 3) from x = -2.5 to x = -0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.3
|
math
|
train
|
math_algebra_func_area_level_3_3_890
|
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|(-1|(1x - 5)| - 2) + 1| + 3) - 3) + 1, g(x) = 1|(-2|(3|x + 3| - 3) - 1| - 3) + 2| + 1, x = -4.0, and x = -1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
13.3
|
math
|
train
|
math_algebra_func_area_level_3_3_891
|
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(1(-3x - 2) + 5)^2 + 2(1(-3x - 2) + 5) - 2) - 3)/(1(-3(1(-3x - 2) + 5)^2 + 2(1(-3x - 2) + 5) - 2) + 2) and g(x) = -2(5(3sin(2πx - 1))^2 + 3(3sin(2πx - 1)) - 1)^2 - 3(5(3sin(2πx - 1))^2 + 3(3sin(2πx - 1)) - 1) - 4 between the vertical lines x = 0.7 and x = 0.7999999999999999. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
29.2
|
math
|
train
|
math_algebra_func_area_level_3_3_892
|
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((-3(4x^2 + 4x) - 3)/(3(4x^2 + 4x) - 2)) + 2)/(3((-3(4x^2 + 4x) - 3)/(3(4x^2 + 4x) - 2)) - 1)) - 1)/(2((-2((-3(4x^2 + 4x) - 3)/(3(4x^2 + 4x) - 2)) + 2)/(3((-3(4x^2 + 4x) - 3)/(3(4x^2 + 4x) - 2)) - 1)) - 1), g(x) = 4(-1sin(2π(-2|x - 1| - 3) + 3) + 3)^2, x = -0.9, and x = -0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
31.3
|
math
|
train
|
math_algebra_func_area_level_3_3_893
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-1(-3|(3cos(2π(-1|x| + 3) + 2) - 2) + 1| + 2))/(-1(-3|(3cos(2π(-1|x| + 3) + 2) - 2) + 1| + 2)) and g(x) = 3sin(3π((-1(-4x + 2) + 1)/(1(-4x + 2) - 2)) - 2) + 1 from x = -0.6 to x = -0.3. 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_894
|
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(-4(-2|x + 1| + 2) - 1) + 3) + 5, g(x) = 2|((3(2x + 1) - 2)/(1(2x + 1))) - 2| - 3, x = -2.8, and x = -0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
32.5
|
math
|
train
|
math_algebra_func_area_level_3_3_895
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -1(2e^(-1(2|(2|x + 3| + 3)| + 2)) - 3)^2 + 5(2e^(-1(2|(2|x + 3| + 3)| + 2)) - 3), g(x) = -2(-3(1x - 3)^2 - 4(1x - 3) + 1)^2 - 1(-3(1x - 3)^2 - 4(1x - 3) + 1) + 1, x = 0.9, and x = 3.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
51.2
|
math
|
train
|
math_algebra_func_area_level_3_3_896
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-3((-2(-5(-4x + 2)^2 + 4) + 1)/(2(-5(-4x + 2)^2 + 4) - 3)) + 3)/(2((-2(-5(-4x + 2)^2 + 4) + 1)/(2(-5(-4x + 2)^2 + 4) - 3)) - 1) and g(x) = -1(-1(-3x + 1)^2 - 4(-3x + 1) - 3) + 1 from x = 0.3 to x = 0.7. 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_897
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 5(-1(2|(3sin(2πx - 1))| - 2) + 5)^2 - 2(-1(2|(3sin(2πx - 1))| - 2) + 5) - 3 and g(x) = 5(-3sin(3π((-2x - 2)/(2x + 2)) + 3) + 3) - 2 from x = 1.5 to x = 1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
23.7
|
math
|
train
|
math_algebra_func_area_level_3_3_898
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1(1((-2((1x - 1)/(2x - 1)) + 1)/(3((1x - 1)/(2x - 1))))) - 3 and g(x) = 1((2(2x - 5) - 2)/(-1(2x - 5) - 1)) + 4 from x = 1.1 to x = 1.5. 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_899
|
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(5(-4x^2 - 3x + 3) - 1) + 5) + 1)/(-2(-3(5(-4x^2 - 3x + 3) - 1) + 5)), g(x) = 5(4((2x + 1)/(3x - 2))^2 + 3((2x + 1)/(3x - 2)) - 4) - 4, x = -1.2, and x = 0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
36.2
|
math
|
train
|
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