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_400
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -2e^(-1(3(3|(-4x - 4) + 2| - 1) - 1)) + 1 and g(x) = -2sin(3π(-4((-1x - 2)/(1x))^2 - 2((-1x - 2)/(1x)) - 3) + 1) - 1 from x = 0.6 to x = 0.7. 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_401
|
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 - 3x + 3) - 1)^2 + 4(1(-1x^2 - 3x + 3) - 1) + 2)^2 - 5(-1(1(-1x^2 - 3x + 3) - 1)^2 + 4(1(-1x^2 - 3x + 3) - 1) + 2) - 3 and g(x) = 4((-2(1x^2 - 2x - 1) + 2)/(-3(1x^2 - 2x - 1) + 2))^2 - 2 from x = -0.2 to x = 0.2. 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_402
|
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(-2|(-2(-3x^2 + 4x + 2)) + 1| + 2) + 1 and g(x) = (3(-1(4x - 4) + 2))/(-2(-1(4x - 4) + 2) - 1) between the vertical lines x = -0.4 and x = -0.2. 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_403
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 2(-1(2|(-2|x - 2| + 3) - 1| - 2)^2 - 4(2|(-2|x - 2| + 3) - 1| - 2)) - 4 and g(x) = -1((-1(-2e^(2x) - 2) - 1)/(-2(-2e^(2x) - 2) + 3)) + 1 from x = 2.7 to x = 3.3. 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_404
|
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(1(3x + 3) + 1)^2 + 1(1(3x + 3) + 1) + 3) - 4, g(x) = 1(-2sin(2π(-3|x - 3| + 3) + 1) + 2)^2 + 3(-2sin(2π(-3|x - 3| + 3) + 1) + 2) - 1, x = -1.8, and x = -1.6. 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_405
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 1|(3cos(3π((1(-5x + 2) + 2)/(-3(-5x + 2))) - 3) - 2)| - 3, g(x) = -4(-2cos(1π((3x + 2)/(-3x + 4)) - 2) + 3) + 4, x = 1.4, and x = 1.5. 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_406
|
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(1cos(3π(-3x + 3) - 3) - 1) - 3)/(-2(1cos(3π(-3x + 3) - 3) - 1) + 3)) + 2, g(x) = (1(-2(-2|x - 3| + 1) + 1))/(1(-2(-2|x - 3| + 1) + 1) + 3), x = 1.1, 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_407
|
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(3π(-3|(-5x + 5) + 3| - 1) - 1) - 3) + 2| - 3 and g(x) = 2(3|((3x - 2)/(-1x - 3)) - 2| + 1)^2 - 4(3|((3x - 2)/(-1x - 3)) - 2| + 1) - 5 between the vertical lines x = -1.2 and x = -1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.6
|
math
|
train
|
math_algebra_func_area_level_3_3_408
|
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(-5(-1|(5x^2 - 1x - 4) - 1| - 2)^2 + 2(-1|(5x^2 - 1x - 4) - 1| - 2) + 1) - 2)/(1(-5(-1|(5x^2 - 1x - 4) - 1| - 2)^2 + 2(-1|(5x^2 - 1x - 4) - 1| - 2) + 1) + 2) and g(x) = -3(-2sin(1π((-2x - 2)/(-2x + 1)) - 2) + 1) - 1 between the vertical lines x = -0.5 and x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.9
|
math
|
train
|
math_algebra_func_area_level_3_3_409
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (1(2sin(1π(3(-2x^2 + 2)^2 + 5(-2x^2 + 2) - 5)) + 1) + 3)/(-3(2sin(1π(3(-2x^2 + 2)^2 + 5(-2x^2 + 2) - 5)) + 1) + 2) and g(x) = 1sin(2π((-2((-1x - 2)/(3x + 2)) - 1)/(3((-1x - 2)/(3x + 2)) - 1)) - 1) from x = -0.4 to x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.0
|
math
|
train
|
math_algebra_func_area_level_3_3_410
|
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((1(-1(-1x^2 - 4x) + 1) - 3)/(-1(-1(-1x^2 - 4x) + 1) + 2))) - 1 and g(x) = -3cos(1π((-1((1x + 3)/(-2x - 2)) - 2)/(-1((1x + 3)/(-2x - 2)))) + 3) - 2 between the vertical lines x = -3.3 and x = -3.1999999999999997. 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_411
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -2(-1cos(1π(-4(-3x^2 - 5x - 1) + 1) - 1) + 2)^2 + 4(-1cos(1π(-4(-3x^2 - 5x - 1) + 1) - 1) + 2) - 3, g(x) = -2|(1(2x - 5) - 2) - 3| - 1, x = 3.2, and x = 3.3000000000000003. 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_412
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 2sin(2π(1(-3(1x^2 - 4x + 1)^2 - 3(1x^2 - 4x + 1))^2 + 5(-3(1x^2 - 4x + 1)^2 - 3(1x^2 - 4x + 1)) - 1) - 3) + 1 and g(x) = -1(-3|((-3x + 2)/(-1x - 2)) + 1| + 3)^2 - 3(-3|((-3x + 2)/(-1x - 2)) + 1| + 3) - 2 from x = -0.5 to x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_3_3_413
|
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(-1sin(2πx + 1)) - 1) + 2)^2 - 1(3(1(-1sin(2πx + 1)) - 1) + 2) + 4, g(x) = 1(-1(-1x^2 + 4x - 1)^2 - 5(-1x^2 + 4x - 1) - 1)^2 + 5(-1(-1x^2 + 4x - 1)^2 - 5(-1x^2 + 4x - 1) - 1) - 3, x = -0.1, and x = 0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
16.4
|
math
|
train
|
math_algebra_func_area_level_3_3_414
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1(-3(2sin(2π((-1x)/(3x + 3)) - 3) - 2) - 2) + 2 and g(x) = -1|(4(-1|x + 1|)^2 + 2(-1|x + 1|) - 3) + 3| + 3 from x = -1.0 to x = -0.9. 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_415
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 2cos(3π(-2((-3((2x + 1)/(1x - 2)) - 1)/(-1((2x + 1)/(1x - 2)) + 3))^2 - 2((-3((2x + 1)/(1x - 2)) - 1)/(-1((2x + 1)/(1x - 2)) + 3)) + 2) - 2) + 2 and g(x) = 2|(1(-1e^(-2x) + 2) + 2) + 3| from x = -1.1 to x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_3_3_416
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 5(1(3((-3x + 3)/(1x - 2)) + 4) + 2)^2 - 4(1(3((-3x + 3)/(1x - 2)) + 4) + 2) - 2 and g(x) = -1|(-1(5x + 5)^2 + 4(5x + 5) - 1) + 3| + 1 from x = -0.9 to x = -0.1. 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_417
|
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(-3|(5x - 4) + 1| - 3) - 2)/(-3(-3|(5x - 4) + 1| - 3) - 1)) - 1) - 3, g(x) = -1cos(2π(5(-1x + 3)^2 - 2(-1x + 3) + 2) - 1) - 1, x = 1.8, and x = 1.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_3_3_418
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1sin(2π(2(-1(3x^2 + 1)^2 + 2(3x^2 + 1) - 4) + 2) - 3) - 3 and g(x) = 1(-3sin(2π(-1|x| + 2) - 3) - 3) + 1 from x = 3.1 to x = 3.2. 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_419
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 2(-2(1(-3x + 3)^2 + 1(-3x + 3) - 4)^2 - 5(1(-3x + 3)^2 + 1(-3x + 3) - 4) + 3) - 2 and g(x) = -3(2(-2e^(-2x) + 2)^2 - 2(-2e^(-2x) + 2) + 3)^2 + 2(2(-2e^(-2x) + 2)^2 - 2(-2e^(-2x) + 2) + 3) + 2 from x = 0.4 to x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
134.8
|
math
|
train
|
math_algebra_func_area_level_3_3_420
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -5(-1sin(1π(5(-3x + 2) + 3) + 3) + 1) - 5 and g(x) = (-2((-2(-3|x + 3| + 3) + 2)/(3(-3|x + 3| + 3) - 1)) - 2)/(-1((-2(-3|x + 3| + 3) + 2)/(3(-3|x + 3| + 3) - 1)) + 2) from x = -3.8 to x = -2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
14.8
|
math
|
train
|
math_algebra_func_area_level_3_3_421
|
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(-5(3|x + 1| - 3) + 4) - 3) - 3 and g(x) = (1((-2((-2x + 3)/(-1x + 2)) - 2)/(3((-2x + 3)/(-1x + 2)) - 2)) - 3)/(3((-2((-2x + 3)/(-1x + 2)) - 2)/(3((-2x + 3)/(-1x + 2)) - 2)) - 1) between the vertical lines x = -2.2 and x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
22.2
|
math
|
train
|
math_algebra_func_area_level_3_3_422
|
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((3(-4((-1x)/(-3x + 4))^2 + 2) + 2)/(1(-4((-1x)/(-3x + 4))^2 + 2) - 3)) - 3) + 2 and g(x) = -2sin(2π((-3(-3x + 1) - 3)/(1(-3x + 1) - 3)) - 1) + 1 between the vertical lines x = 0.9 and 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_423
|
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(-5((-2x)/(2x - 1)) + 5)^2 - 2(-5((-2x)/(2x - 1)) + 5))| + 1 and g(x) = 3sin(3π(4(-3|x - 2| - 3)^2 - 5(-3|x - 2| - 3) + 3) + 1) - 2 between the vertical lines x = 0.2 and x = 0.30000000000000004. 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_424
|
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 - 1)/(3x + 3)) + 3| - 2) + 2)/(-2(1|((3x - 1)/(3x + 3)) + 3| - 2) - 1))^2 - 4((1(1|((3x - 1)/(3x + 3)) + 3| - 2) + 2)/(-2(1|((3x - 1)/(3x + 3)) + 3| - 2) - 1)), g(x) = 2(-3e^(-1(1|x - 2| - 2)) + 2)^2 + 1(-3e^(-1(1|x - 2| - 2)) + 2) + 1, x = -0.8, and x = -0.7000000000000001. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
10.4
|
math
|
train
|
math_algebra_func_area_level_3_3_425
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -2|((-3((-2(-2sin(3πx + 2) + 2))/(2(-2sin(3πx + 2) + 2))))/(3((-2(-2sin(3πx + 2) + 2))/(2(-2sin(3πx + 2) + 2))) - 1)) + 2| + 1 and g(x) = -1|(1cos(1π(3|x + 1| + 1) - 2) - 1) - 1| from x = 0.3 to x = 0.8. 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_426
|
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|((-3(3x^2 + 3x + 2) + 2)/(-3(3x^2 + 3x + 2) + 4)) - 1|)^2 - 5(-1|((-3(3x^2 + 3x + 2) + 2)/(-3(3x^2 + 3x + 2) + 4)) - 1|) + 5 and g(x) = 5(-1(2|x - 1| - 2)^2 - 1(2|x - 1| - 2) + 4)^2 - 3(-1(2|x - 1| - 2)^2 - 1(2|x - 1| - 2) + 4) + 3 between the vertical lines x = 2.6 and x = 2.8. 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_427
|
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(1x^2 + 5x + 5) - 1)/(-2(1x^2 + 5x + 5) - 2)) - 2)/(3((1(1x^2 + 5x + 5) - 1)/(-2(1x^2 + 5x + 5) - 2)) - 2)) + 4 and g(x) = -1(-1sin(1π((-1x - 3)/(-3x + 4)) - 2) + 3) - 3 between the vertical lines x = -3.5 and x = -1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
19.4
|
math
|
train
|
math_algebra_func_area_level_3_3_428
|
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^2 + 2x + 5) + 3| + 2)^2 - 4(-1|(-1x^2 + 2x + 5) + 3| + 2) + 5) - 1)/(-1(1(-1|(-1x^2 + 2x + 5) + 3| + 2)^2 - 4(-1|(-1x^2 + 2x + 5) + 3| + 2) + 5)) and g(x) = 2(1(-1x - 5) + 3) - 2 between the vertical lines x = -1.9 and x = -1.6. 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_429
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-1((2(2(3|x| + 3) - 2) + 3)/(-1(2(3|x| + 3) - 2) + 2)) - 2)/(-2((2(2(3|x| + 3) - 2) + 3)/(-1(2(3|x| + 3) - 2) + 2)) - 3) and g(x) = -2|(3(1|x| - 3)^2 + 4(1|x| - 3) - 1) + 2| + 3 from x = 1.6 to x = 3.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.9
|
math
|
train
|
math_algebra_func_area_level_3_3_430
|
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(3e^(2(2|x| - 2)) - 1)^2 + 5(3e^(2(2|x| - 2)) - 1)) + 5 and g(x) = (-3(1sin(2π((-3x)/(-2x - 1)) - 3) - 1) + 2)/(-2(1sin(2π((-3x)/(-2x - 1)) - 3) - 1) + 3) between the vertical lines x = 0.7 and x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
10.5
|
math
|
train
|
math_algebra_func_area_level_3_3_431
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 2(1((-3(1|x + 2| - 1) - 3)/(1(1|x + 2| - 1)))^2 + 5((-3(1|x + 2| - 1) - 3)/(1(1|x + 2| - 1))) - 2)^2 - 5(1((-3(1|x + 2| - 1) - 3)/(1(1|x + 2| - 1)))^2 + 5((-3(1|x + 2| - 1) - 3)/(1(1|x + 2| - 1))) - 2) + 1 and g(x) = 3cos(1π(-1((2x - 2)/(-2x))^2 + 1((2x - 2)/(-2x)) - 4) + 3) - 3 from x = 0.2 to x = 0.30000000000000004. 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_432
|
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(-4(3|x| - 1)^2 - 3(3|x| - 1) + 1) + 3) - 1| - 3, g(x) = -4(1((-3x + 1)/(1x - 3))^2 + 4((-3x + 1)/(1x - 3)) - 2) + 4, x = 2.5, and x = 3.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
-2411.4
|
math
|
train
|
math_algebra_func_area_level_3_3_433
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -3sin(1π(2((3(1x^2 + 4x - 4) - 1)/(-1(1x^2 + 4x - 4) + 2))^2 + 1((3(1x^2 + 4x - 4) - 1)/(-1(1x^2 + 4x - 4) + 2)) + 2) - 1) - 2 and g(x) = (2(-1|(2x^2 + 5x - 1) - 3| + 1) + 1)/(3(-1|(2x^2 + 5x - 1) - 3| + 1) + 2) from x = -4.5 to x = -4.3. 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_434
|
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(2|(-2|((1x + 3)/(2x + 3)) + 1|) - 2|) - 1) + 2 and g(x) = (-3(1e^(2(-2x + 1)) - 3) - 3)/(-2(1e^(2(-2x + 1)) - 3) + 3) between the vertical lines x = -1.3 and x = -1.2. 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_435
|
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((1((-2x + 2)/(3x + 2)) + 1)/(-1((-2x + 2)/(3x + 2)) + 3)) - 2) - 1)/(-2(1((1((-2x + 2)/(3x + 2)) + 1)/(-1((-2x + 2)/(3x + 2)) + 3)) - 2) - 2) and g(x) = (-2(1(1|x + 2| - 3) + 2))/(-3(1(1|x + 2| - 3) + 2) - 2) between the vertical lines x = -1.4 and x = -0.2. 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_436
|
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 - 1| + 3)^2 - 5(1|x - 1| + 3) - 5)^2 + 3(-2(1|x - 1| + 3)^2 - 5(1|x - 1| + 3) - 5) - 2))/(2(-1(-2(1|x - 1| + 3)^2 - 5(1|x - 1| + 3) - 5)^2 + 3(-2(1|x - 1| + 3)^2 - 5(1|x - 1| + 3) - 5) - 2) - 1) and g(x) = 2(-3cos(3π(-3x + 4) + 2) - 2)^2 - 5(-3cos(3π(-3x + 4) + 2) - 2) + 1 between the vertical lines x = -0.3 and x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.5
|
math
|
train
|
math_algebra_func_area_level_3_3_437
|
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 + 1)^2 - 2(-4x + 1) + 1) - 3| + 3)^2 - 4(-3|(-2(-4x + 1)^2 - 2(-4x + 1) + 1) - 3| + 3) + 2 and g(x) = (-2(4(-5x - 1) - 5))/(2(4(-5x - 1) - 5) - 1) between the vertical lines x = 0.3 and x = 0.5. 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_438
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -3((1((-1((1x - 2)/(-1x + 2)) + 2)/(1((1x - 2)/(-1x + 2)) + 1)) + 3)/(3((-1((1x - 2)/(-1x + 2)) + 2)/(1((1x - 2)/(-1x + 2)) + 1)) - 2))^2 + 2((1((-1((1x - 2)/(-1x + 2)) + 2)/(1((1x - 2)/(-1x + 2)) + 1)) + 3)/(3((-1((1x - 2)/(-1x + 2)) + 2)/(1((1x - 2)/(-1x + 2)) + 1)) - 2)) - 1 and g(x) = -1(-1e^(-2(-2|x + 1| + 3)))^2 - 4(-1e^(-2(-2|x + 1| + 3))) + 4 from x = -2.9 to x = 0.9. 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_439
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 3(-2|(-3(-2e^(-2x) + 3) - 2) + 3| + 2) + 1 and g(x) = -1(-2(-1e^(-1x) + 3)^2 + 3(-1e^(-1x) + 3) - 1) - 4 from x = -0.2 to x = -0.0. 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_440
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (1(3sin(3π((1(4x + 1) + 2)/(2(4x + 1) - 1)) - 3) + 2))/(2(3sin(3π((1(4x + 1) + 2)/(2(4x + 1) - 1)) - 3) + 2) + 2) and g(x) = (1(-5(-2|x - 2| - 1)^2 + 3(-2|x - 2| - 1) + 4) + 3)/(-2(-5(-2|x - 2| - 1)^2 + 3(-2|x - 2| - 1) + 4) + 3) from x = -0.4 to 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_441
|
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|(2(-2((2x + 1)/(-3x - 3))^2 - 2((2x + 1)/(-3x - 3)) + 4) - 2) + 3| and g(x) = 5(2sin(1π(2|x + 1| - 3) - 1) - 2)^2 - 3(2sin(1π(2|x + 1| - 3) - 1) - 2) + 5 between the vertical lines x = -2.1 and x = -1.7. 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_442
|
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(2|(-5x + 1) + 2| - 2)^2 + 1(2|(-5x + 1) + 2| - 2))^2 - 5(-2(2|(-5x + 1) + 2| - 2)^2 + 1(2|(-5x + 1) + 2| - 2)) - 4, g(x) = -1(3|(-1e^(-1x) - 1) - 1| + 3)^2 - 3(3|(-1e^(-1x) - 1) - 1| + 3) + 5, x = 0.1, and x = 1.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
126.0
|
math
|
train
|
math_algebra_func_area_level_3_3_443
|
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(1(4x^2 - 1x + 2)^2 - 4) + 5) + 1, g(x) = 2(-1|(-3cos(3πx + 3) + 1) + 3| - 1)^2 - 2, x = 0.3, and x = 0.4. 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_444
|
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|(4(1|x - 2| - 3) - 2) - 3| - 1) - 1, g(x) = -2cos(1π(-2|(-1|x - 1| + 2) + 1|) + 3) - 1, x = -2.4, and x = -2.2. 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_445
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (3(3(1|((-3x + 2)/(1x)) - 2| - 3) + 1) + 3)/(-1(3(1|((-3x + 2)/(1x)) - 2| - 3) + 1) + 3) and g(x) = (-2(-2|(-2|x - 2| + 1)| + 1) + 1)/(-1(-2|(-2|x - 2| + 1)| + 1) - 1) from x = 0.2 to x = 2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
133.6
|
math
|
train
|
math_algebra_func_area_level_3_3_446
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1((2(-3(1|x - 3| - 1) + 3) + 1)/(3(-3(1|x - 3| - 1) + 3) + 1)) + 2 and g(x) = -2(-1(3sin(3πx + 3)))^2 + 4 from x = -4.0 to x = -3.7. 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_447
|
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(1x + 2) + 1) + 1| - 3)^2 - 4 and g(x) = -3((-1(2|x - 2| - 1) + 1)/(2(2|x - 2| - 1) + 2)) - 2 between the vertical lines x = -2.9 and x = -2.1. 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_448
|
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(1cos(2π(-5(-5x^2 - 3x)^2 + 5(-5x^2 - 3x) - 2) + 3) + 2)^2 + 1(1cos(2π(-5(-5x^2 - 3x)^2 + 5(-5x^2 - 3x) - 2) + 3) + 2) - 3 and g(x) = 2|(-2(5x + 1) + 3) + 1| + 1 between the vertical lines x = 0.4 and x = 0.5. 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_449
|
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(3(-2x))^2 - 5(3(-2x)) - 4)^2 - 4(-2(3(-2x))^2 - 5(3(-2x)) - 4) - 3, g(x) = -3|((3(4x^2 - 4) + 1)/(2(4x^2 - 4) - 1)) - 3| - 1, x = 0.1, and x = 0.3. 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_450
|
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(-5x^2 + 3x + 4) + 4) - 1)/(3(3(-5x^2 + 3x + 4) + 4))) - 3| - 1, g(x) = -1((-1(5x - 2) + 3)/(1(5x - 2) + 2)) + 4, x = -0.7, and x = 1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
30.9
|
math
|
train
|
math_algebra_func_area_level_3_3_451
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1(3|(-1((2x + 2)/(1x - 2)) - 2) - 2| - 2)^2 + 1(3|(-1((2x + 2)/(1x - 2)) - 2) - 2| - 2) - 5 and g(x) = (3(-4(-3sin(3πx + 2) - 3)^2 - 5(-3sin(3πx + 2) - 3) - 2) - 1)/(1(-4(-3sin(3πx + 2) - 3)^2 - 5(-3sin(3πx + 2) - 3) - 2) + 3) from x = 0.7 to x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.7
|
math
|
train
|
math_algebra_func_area_level_3_3_452
|
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(-2(-3sin(3π(-4x + 3) - 1) + 1)^2 + 2(-3sin(3π(-4x + 3) - 1) + 1) - 1) - 3)/(-1(-2(-3sin(3π(-4x + 3) - 1) + 1)^2 + 2(-3sin(3π(-4x + 3) - 1) + 1) - 1) + 2) and g(x) = 2|(2|(1x^2 - 4x + 3) - 3| + 2) - 2| - 3 between the vertical lines x = 0.1 and x = 3.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
38.2
|
math
|
train
|
math_algebra_func_area_level_3_3_453
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -2(-3(3|(-2cos(2πx) - 1) + 1| + 3) - 5) and g(x) = 3(2|(-5x^2 + 5x - 3) + 2| + 3)^2 + 2(2|(-5x^2 + 5x - 3) + 2| + 3) + 5 from x = 0.3 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.8
|
math
|
train
|
math_algebra_func_area_level_3_3_454
|
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(-4(2|x + 2| + 2) + 2) + 1)/(-1(-4(2|x + 2| + 2) + 2) - 1)) + 3)/(1((1(-4(2|x + 2| + 2) + 2) + 1)/(-1(-4(2|x + 2| + 2) + 2) - 1)) - 3), g(x) = (2(1(-3x^2 + 3x + 1)^2 + 3(-3x^2 + 3x + 1) - 4) - 1)/(3(1(-3x^2 + 3x + 1)^2 + 3(-3x^2 + 3x + 1) - 4) + 1), x = -0.9, and x = 0.0. 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_455
|
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|(-2|x - 2| + 2) + 3| + 1) - 1) + 1)^2 - 1(2cos(2π(-3|(-2|x - 2| + 2) + 3| + 1) - 1) + 1) + 5 and g(x) = (-3((3(2|x + 2| + 2) - 1)/(-1(2|x + 2| + 2) - 1)) + 3)/(1((3(2|x + 2| + 2) - 1)/(-1(2|x + 2| + 2) - 1)) + 2) between the vertical lines x = -2.0 and x = -1.9. 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_456
|
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(-2sin(3π(1(1x^2 + 3x - 3)^2 + 3(1x^2 + 3x - 3) - 3) - 3) + 2)^2 + 5 and g(x) = (-2(-1|((3x + 1)/(1x + 3)) + 3| + 1) + 2)/(-1(-1|((3x + 1)/(1x + 3)) + 3| + 1)) between the vertical lines x = -1.9 and x = -1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
28.9
|
math
|
train
|
math_algebra_func_area_level_3_3_457
|
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((-2((-1x + 3)/(-2x + 1)) - 2)/(1((-1x + 3)/(-2x + 1))))^2 - 1((-2((-1x + 3)/(-2x + 1)) - 2)/(1((-1x + 3)/(-2x + 1))))) + 2)/(3(-4((-2((-1x + 3)/(-2x + 1)) - 2)/(1((-1x + 3)/(-2x + 1))))^2 - 1((-2((-1x + 3)/(-2x + 1)) - 2)/(1((-1x + 3)/(-2x + 1))))) - 2), g(x) = -3|(-2|((2x - 2)/(2x + 1)) - 3|) + 1| + 1, x = -1.7, and x = -1.3. 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_458
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -2(1|((2(3|x - 1| - 1) + 3)/(-2(3|x - 1| - 1) + 3)) - 1| - 3) + 3 and g(x) = 1|(1sin(2π(-1x + 3) + 2) - 2) + 2| + 2 from x = 1.6 to x = 2.7. Round 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_459
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -2|((-2((1(-1|x| + 3) + 2)/(-3(-1|x| + 3) - 1)) - 1)/(-1((1(-1|x| + 3) + 2)/(-3(-1|x| + 3) - 1)) + 2)) - 1| - 1 and g(x) = (2(4(-2e^(-2x) + 3)) - 2)/(-2(4(-2e^(-2x) + 3)) + 3) from x = 3.1 to x = 3.2. 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_460
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -1|(4((2(2sin(3πx - 1) + 1) - 2)/(1(2sin(3πx - 1) + 1) + 2)) + 2) - 1| + 2, g(x) = (1((-1((2x - 3)/(2x + 2)) + 1)/(-1((2x - 3)/(2x + 2)))) + 3)/(-3((-1((2x - 3)/(2x + 2)) + 1)/(-1((2x - 3)/(2x + 2)))) + 4), x = 4.1, and x = 4.4. 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_461
|
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|(-5x^2 - 4x)| + 2) + 2| - 2) - 2) + 1, g(x) = 1(-3((-1x + 3)/(2x + 1)) + 2) + 1, x = 1.3, and x = 1.4000000000000001. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_3_3_462
|
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(-3(-2x + 4)^2 + 1(-2x + 4) - 5) + 1) + 2)/(3(4(-3(-2x + 4)^2 + 1(-2x + 4) - 5) + 1)) and g(x) = -3cos(1π(1|(5x^2 - 2) - 1| + 1) + 1) + 2 between the vertical lines x = -4.1 and x = -3.9999999999999996. 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_463
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 5(-3|(-5(3x) - 3) + 1| - 1)^2 + 5(-3|(-5(3x) - 3) + 1| - 1) - 2 and g(x) = (-2(-3|(1sin(2πx + 1) - 2) + 2|))/(-1(-3|(1sin(2πx + 1) - 2) + 2|) - 2) from x = -0.1 to x = -0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
20.6
|
math
|
train
|
math_algebra_func_area_level_3_3_464
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -3|(2(3|((-3x)/(1x + 1)) - 3| - 3)) - 2| + 3 and g(x) = 4(-1e^(-1(2x + 2)) - 2) + 5 from x = -0.6 to x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.4
|
math
|
train
|
math_algebra_func_area_level_3_3_465
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -2|(2(-2(5x - 1)^2 + 1(5x - 1) + 3) + 5) + 1| + 3 and g(x) = (3(4(-3x - 5) - 1) + 1)/(3(4(-3x - 5) - 1) - 2) from x = -0.1 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
10.1
|
math
|
train
|
math_algebra_func_area_level_3_3_466
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 2cos(2π((-3(-2|(-1|x - 1|) + 3| + 2) - 3)/(-3(-2|(-1|x - 1|) + 3| + 2) - 1))) and g(x) = (2(5(-2cos(3πx - 3) + 3) - 1) + 1)/(-1(5(-2cos(3πx - 3) + 3) - 1) - 2) from x = -0.6 to 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_467
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (1(1|(1(-4x - 2)^2 + 5(-4x - 2) + 5) + 3|) - 1)/(2(1|(1(-4x - 2)^2 + 5(-4x - 2) + 5) + 3|) - 1) and g(x) = 1(-3(-3x - 2)^2 + 3(-3x - 2))^2 + 3(-3(-3x - 2)^2 + 3(-3x - 2)) - 5 from x = -1.3 to x = -0.4. Round 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_468
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1(3|(1(5x + 1)^2 - 5(5x + 1) - 3) - 1| + 3)^2 + 5(3|(1(5x + 1)^2 - 5(5x + 1) - 3) - 1| + 3) + 5 and g(x) = -5(3sin(3π(-2x^2 - 2x + 5) - 1)) - 1 from x = -0.4 to x = -0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.9
|
math
|
train
|
math_algebra_func_area_level_3_3_469
|
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((1(-5x - 2) + 3)/(-2(-5x - 2) - 3)))/(-1((1(-5x - 2) + 3)/(-2(-5x - 2) - 3)) + 2)) - 5 and g(x) = -3|(3sin(3π(1x^2 + 2x + 4) - 1) + 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}"
]
}
|
0.4
|
math
|
train
|
math_algebra_func_area_level_3_3_470
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1(-2(-2(-3x^2 + 3x + 3)^2 - 1(-3x^2 + 3x + 3) - 4) - 2) - 2 and g(x) = (2(3sin(2π(-5x^2 + 4x + 2) - 2)) - 1)/(1(3sin(2π(-5x^2 + 4x + 2) - 2)) - 2) from x = 0.5 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
17.3
|
math
|
train
|
math_algebra_func_area_level_3_3_471
|
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(3sin(2π(1x + 1)) - 1)^2 + 5(3sin(2π(1x + 1)) - 1) - 1) - 2| - 2, g(x) = (3(1|(-1cos(2πx - 3) - 3) + 3| + 3) + 2)/(1(1|(-1cos(2πx - 3) - 3) + 3| + 3) + 2), x = 0.4, and x = 0.5. 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_472
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-3(3cos(3π(-5(2|x + 1| - 2)^2 - 2(2|x + 1| - 2) + 3) + 2) + 1) + 2)/(1(3cos(3π(-5(2|x + 1| - 2)^2 - 2(2|x + 1| - 2) + 3) + 2) + 1) - 2), g(x) = (-2((1((1x - 1)/(3x - 2)) + 3)/(-1((1x - 1)/(3x - 2)) + 3)) - 1)/(-1((1((1x - 1)/(3x - 2)) + 3)/(-1((1x - 1)/(3x - 2)) + 3)) - 2), x = -4.8, and x = -4.7. 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_473
|
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(2sin(2πx + 3)) + 1)/(2(2sin(2πx + 3)) - 1)) + 1)/(1((-1(2sin(2πx + 3)) + 1)/(2(2sin(2πx + 3)) - 1)) - 3))^2 - 5((-3((-1(2sin(2πx + 3)) + 1)/(2(2sin(2πx + 3)) - 1)) + 1)/(1((-1(2sin(2πx + 3)) + 1)/(2(2sin(2πx + 3)) - 1)) - 3)), g(x) = (2(-3e^(2(1x^2 - 1x + 4)) + 2) + 3)/(-2(-3e^(2(1x^2 - 1x + 4)) + 2) - 2), x = -0.0, and x = 0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
15.0
|
math
|
train
|
math_algebra_func_area_level_3_3_474
|
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(-2|(1e^(2x) - 3) + 1| + 3)^2 + 2(-2|(1e^(2x) - 3) + 1| + 3) - 4) - 3)/(3(4(-2|(1e^(2x) - 3) + 1| + 3)^2 + 2(-2|(1e^(2x) - 3) + 1| + 3) - 4)), g(x) = -3sin(1π(-2|(1x + 3) - 1| - 1) - 1) + 2, 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_475
|
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|(5((1x + 3)/(-2x + 3)) + 5) - 1| - 1)^2 - 2(1|(5((1x + 3)/(-2x + 3)) + 5) - 1| - 1) + 2, g(x) = -3|((2(-4x + 3))/(2(-4x + 3) + 3)) + 3|, x = 1.1, and x = 3.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
-1161.1
|
math
|
train
|
math_algebra_func_area_level_3_3_476
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -5((1(2cos(1π(4x^2 - 1x + 2) + 3) - 3) - 3)/(-1(2cos(1π(4x^2 - 1x + 2) + 3) - 3))), g(x) = 1(3|(-5x^2 + 2x + 4) - 3| + 1) + 2, x = 1.1, and x = 1.2. 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_477
|
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(3π((2(-1(1|x| - 1) + 5) - 1)/(1(-1(1|x| - 1) + 5))) + 1) + 3 and g(x) = 1(-2|(1x^2 + 5x + 4) + 1| + 1)^2 + 5(-2|(1x^2 + 5x + 4) + 1| + 1) - 5 between the vertical lines x = -4.7 and x = -0.3. 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_478
|
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(-2cos(3π((-2(-2|x - 2| + 3) - 3)/(3(-2|x - 2| + 3) - 2)) + 1) - 2) - 1)/(-2(-2cos(3π((-2(-2|x - 2| + 3) - 3)/(3(-2|x - 2| + 3) - 2)) + 1) - 2) + 3) and g(x) = -5((-1(1x + 4) + 2)/(-2(1x + 4) + 3))^2 + 1((-1(1x + 4) + 2)/(-2(1x + 4) + 3)) + 4 between the vertical lines x = -3.0 and x = -2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
-4.2
|
math
|
train
|
math_algebra_func_area_level_3_3_479
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -3cos(1π(-1(3((-3x + 2)/(-3x - 2)) + 2)^2 + 5) - 3) - 2 and g(x) = -3|(-1e^(1(-4x + 2)) - 1)| - 1 from x = 2.4 to x = 2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_3_3_480
|
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(5(-2cos(3πx + 3) + 2)^2 - 5(-2cos(3πx + 3) + 2) - 3) + 4) - 2, g(x) = 2|((2((2x - 1)/(-2x - 1)) - 3)/(2((2x - 1)/(-2x - 1)) - 3)) + 3| + 1, x = -1.8, and x = -1.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
11.9
|
math
|
train
|
math_algebra_func_area_level_3_3_481
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -5((1(2e^(-1(1|x + 3| - 3)) - 2) + 1)/(-3(2e^(-1(1|x + 3| - 3)) - 2) + 1)) + 5 and g(x) = (-1(-3(-2cos(3πx - 1) - 1)^2 + 2(-2cos(3πx - 1) - 1) + 3) + 3)/(2(-3(-2cos(3πx - 1) - 1)^2 + 2(-2cos(3πx - 1) - 1) + 3) + 2) from x = -1.4 to x = -1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.2
|
math
|
train
|
math_algebra_func_area_level_3_3_482
|
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(-3x^2 + 5x - 2)^2 + 1(-3x^2 + 5x - 2) + 4) - 2| + 2) - 3)/(2(-1|(-4(-3x^2 + 5x - 2)^2 + 1(-3x^2 + 5x - 2) + 4) - 2| + 2)) and g(x) = 5(-2|(1|x + 2| + 1) + 1| - 2) + 4 between the vertical lines x = 0.6 and x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
103.2
|
math
|
train
|
math_algebra_func_area_level_3_3_483
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -2|(3cos(3π((-1(-1x + 3) - 1)/(-1(-1x + 3) - 2)) - 3) - 2) + 3| and g(x) = (-1(-3cos(1π(5x^2 + 5x - 2) - 2)) - 3)/(3(-3cos(1π(5x^2 + 5x - 2) - 2)) - 2) from x = -2.4 to x = -2.3. 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_484
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 2(2cos(2π(3((1x + 1)/(2x))^2 + 5) + 1)) - 4, g(x) = -5((-3(1x^2 - 5x + 3) + 2)/(3(1x^2 - 5x + 3) + 1)) - 4, 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_485
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1(4(2((2x - 3)/(-1x)) - 1)^2 - 5(2((2x - 3)/(-1x)) - 1) + 1) + 3 and g(x) = -4(1(-3|x - 3| + 1) - 4) + 1 from x = 0.7 to x = 1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
25.0
|
math
|
train
|
math_algebra_func_area_level_3_3_486
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -3sin(3π(-2|(1(-1x^2 - 5x) + 2) + 2| - 1) - 1) + 1, g(x) = -3cos(3π((-1((3x + 3)/(1x - 3)) - 3)/(2((3x + 3)/(1x - 3)))) + 1) + 3, x = -1.8, and x = -1.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.5
|
math
|
train
|
math_algebra_func_area_level_3_3_487
|
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(-1cos(2π(-2|(-2|x - 3|)| - 3) - 3) - 2) - 4 and g(x) = -1e^(-2(5(5x + 1)^2 + 4(5x + 1) - 4)) + 1 between the vertical lines x = -1.0 and x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_3_3_488
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -4(4(2(-5x - 1)^2 - 4(-5x - 1) + 3) - 4) + 4 and g(x) = 1(-1|(2e^(2x) - 2) - 2|) + 3 from x = -0.5 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_489
|
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|(3sin(1π(-1x^2 - 4x - 2) + 1) - 3) - 3| + 3) + 2)/(-3(-3|(3sin(1π(-1x^2 - 4x - 2) + 1) - 3) - 3| + 3) - 1) and g(x) = -3cos(3π((-2((-2x - 1)/(2x - 3)) - 1)/(-1((-2x - 1)/(2x - 3)))) - 1) between the vertical lines x = -3.2 and x = -2.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.4
|
math
|
train
|
math_algebra_func_area_level_3_3_490
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -4((-1(5(-4x - 1) + 3) - 3)/(-3(5(-4x - 1) + 3) - 2))^2 - 1((-1(5(-4x - 1) + 3) - 3)/(-3(5(-4x - 1) + 3) - 2)) and g(x) = 1(3|(2x - 3) + 2|)^2 + 4(3|(2x - 3) + 2|) - 1 from x = 0.5 to 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_491
|
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|(3sin(1π(-4x^2 + 2x + 2) + 2)) - 1| - 1) - 2, g(x) = -2|(-3sin(3π(-4x^2 - 4x + 2) + 2) + 3) + 3| - 1, x = 3.0, and x = 3.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.5
|
math
|
train
|
math_algebra_func_area_level_3_3_492
|
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(-1x^2 + 3x + 2)^2 - 2(-1x^2 + 3x + 2) + 3)) - 2)/(3(1(-3(-1x^2 + 3x + 2)^2 - 2(-1x^2 + 3x + 2) + 3)) + 1), g(x) = -1(-1(1cos(2πx + 2) - 3)^2 - 4(1cos(2πx + 2) - 3) - 2) + 4, x = -0.9, and x = -0.3. 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_493
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 2(-2(2|((-2x - 1)/(-1x + 2)) + 3|))^2 + 4(-2(2|((-2x - 1)/(-1x + 2)) + 3|)) - 3 and g(x) = 1e^(-1(1(-3x^2 - 5)^2 + 4(-3x^2 - 5) + 3)) - 1 from x = 0.9 to x = 1.1. 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_494
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3cos(2π((3(-4((-2x - 3)/(-3x + 2))^2 - 4((-2x - 3)/(-3x + 2)) + 5) + 2)/(-3(-4((-2x - 3)/(-3x + 2))^2 - 4((-2x - 3)/(-3x + 2)) + 5) - 3))) - 3, g(x) = (3(-1|(-2x + 3) - 3| - 1) + 2)/(1(-1|(-2x + 3) - 3| - 1) + 2), 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_495
|
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|(5x + 1) + 1| - 1)| - 3) - 2)/(-2(2|(3|(5x + 1) + 1| - 1)| - 3) - 3) and g(x) = -3sin(2π(1(-2x^2 - 4x + 3) - 1)) - 3 between the vertical lines x = 3.9 and x = 4.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_3_3_496
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3e^(1((3(-1(-1x^2 - 4x - 4)) - 3)/(2(-1(-1x^2 - 4x - 4)) + 1))) + 1, g(x) = 2|((2(-4x^2 - 3) - 1)/(-1(-4x^2 - 3) - 2)) + 2| + 2, x = -2.7, and x = -1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.8
|
math
|
train
|
math_algebra_func_area_level_3_3_497
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-1(1(-3(2e^(1x) + 1)^2 - 5(2e^(1x) + 1)) + 2))/(-2(1(-3(2e^(1x) + 1)^2 - 5(2e^(1x) + 1)) + 2) - 3) and g(x) = -2|(3cos(2π(-5x - 1)))| + 3 from x = -1.8 to x = -1.7. 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_498
|
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(-2sin(1π(-4((1x + 1)/(-2x + 3))^2 + 5) - 3) + 3)^2 - 2(-2sin(1π(-4((1x + 1)/(-2x + 3))^2 + 5) - 3) + 3) + 1 and g(x) = 5(-1(3x - 2)^2 + 2(3x - 2) + 1) - 4 between the vertical lines x = 1.6 and x = 1.7000000000000002. Round 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_499
|
algebra_func_area3
|
medium (level 2,3)
| 3 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 3|(-1|((2(2x^2 + 5x + 5) - 1)/(3(2x^2 + 5x + 5) + 3)) + 1| - 3) + 3| and g(x) = -1(1(1x - 3)^2 + 5(1x - 3)) + 5 from x = -2.1 to x = 3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
23.2
|
math
|
train
|
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