messages listlengths 1 1 | ground_truth stringlengths 3 6 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2|(1(-4x^2 + 4x - 3) - 3) + 3| - 2, g(x) = -3(2sin(1πx - 3) - 1)^2 + 4(2sin(1πx - 3) - 1) - 1, x = 2.2, and x = 2.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | 0.9 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2((2(1cos(3πx + 3) + 3) + 3)/(-3(1cos(3πx + 3) + 3) - 3)) + 4 and g(x) = 4(1x^2 + 4x + 4)^2 + 4(1x^2 + 4x + 4) - 1 between the vertical lines x = -2.8 and x = -1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\... | 3.8 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-1(-4(-2cos(2πx + 1) + 2)^2 + 4) + 1)/(2(-4(-2cos(2πx + 1) + 2)^2 + 4) - 1) and g(x) = -5(-2|x - 2| + 2) - 3 from x = 3.0 to x = 3.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 0.3 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1|(4(3x^2 + 1x - 3)) - 3| - 3 and g(x) = 1|(-2cos(2πx + 1) + 1) - 1| - 2 from x = -1.2 to x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 18.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 4((1(2e^(-2x) + 3) - 2)/(1(2e^(-2x) + 3) + 3))^2 - 5((1(2e^(-2x) + 3) - 2)/(1(2e^(-2x) + 3) + 3)) + 2 and g(x) = (2(-2|x - 3| + 1) + 1)/(-1(-2|x - 3| + 1) - 3) between the vertical lines x = 1.8 and x = 4.2. Round to 1 decimal place... | 3.3 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|(2(2x^2 - 2x - 1)^2 + 3(2x^2 - 2x - 1) + 5) + 2| and g(x) = -1(3cos(3πx + 1) - 3)^2 - 1(3cos(3πx + 1) - 3) between the vertical lines x = -0.6 and x = -0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed... | 4.0 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 5(4(5x^2 + 1x - 4)^2 + 4(5x^2 + 1x - 4))^2 - 2(4(5x^2 + 1x - 4)^2 + 4(5x^2 + 1x - 4)) - 5 and g(x) = (3((-1x - 3)/(1x)) + 1)/(-2((-1x - 3)/(1x)) + 3) between the vertical lines x = 0.7 and x = 0.8. Round to 1 decimal place.\n\nPrese... | 0.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-1((-3(-1cos(1πx + 1) + 1))/(1(-1cos(1πx + 1) + 1) + 2)))/(1((-3(-1cos(1πx + 1) + 1))/(1(-1cos(1πx + 1) + 1) + 2))) and g(x) = -3(-1|x + 3|) - 3 from x = -3.7 to x = -2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\b... | 1.3 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3((-1(3|x| - 2))/(3(3|x| - 2) - 2)) - 3 and g(x) = 2e^(1(-1x - 2)) + 3 from x = -0.9 to x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20.8 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1e^(-1(1|(2x - 3) - 1| + 2)) + 1 and g(x) = 1|(5x) + 1| - 2 between the vertical lines x = -0.8 and x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.8 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-2(-1|(-1x^2 + 2x + 2) + 1|) + 3)/(-1(-1|(-1x^2 + 2x + 2) + 1|) + 2), g(x) = 2cos(3π((-1x)/(3x + 1)) + 3) + 2, x = -0.4, and x = -0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 0.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|(2|(4x - 1) - 3| + 1) + 1| - 1 and g(x) = -3|(-2sin(2πx + 1) + 1) + 2| - 2 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}",
"role": "use... | 0.6 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1cos(1π(3|(-2x - 2) - 2| + 1)) - 3 and g(x) = -1(3|x - 1| - 3) + 2 from x = 4.0 to x = 4.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1((-3(-1x^2 + 1x + 2) + 2)/(2(-1x^2 + 1x + 2) + 2)) - 3 and g(x) = -1|((-1x - 2)/(-2x + 3)) - 1| + 1 from x = 2.0 to x = 2.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1(-1(-2|x - 3| + 3)^2 + 5(-2|x - 3| + 3) + 5)^2 + 2(-1(-2|x - 3| + 3)^2 + 5(-2|x - 3| + 3) + 5) - 5, g(x) = -3|(-2|x - 2|) - 2| + 2, x = 1.0, and x = 1.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{... | 1.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1e^(-1(-3(-2|x - 3| + 1) + 4)) + 2 and g(x) = 2|(-4x - 2)| - 3 between the vertical lines x = -1.1 and x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1(-4(1x^2 - 3x + 2) - 2) + 4 and g(x) = -5(-2sin(3πx - 3) + 2)^2 + 5(-2sin(3πx - 3) + 2) from x = 2.6 to x = 3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11.9 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 4(1(-1cos(1πx + 2) - 1)^2 + 1(-1cos(1πx + 2) - 1) - 2) + 2 and g(x) = (-1(3cos(1πx - 3)) - 2)/(-2(3cos(1πx - 3)) + 3) between the vertical lines x = -2.4 and x = -1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format:... | 5.4 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (2(1cos(3π(-2|x - 3| - 2)) + 3))/(-2(1cos(3π(-2|x - 3| - 2)) + 3) - 1), g(x) = 3cos(2π(3x^2 - 4x + 1) - 1) - 3, x = 2.7, and x = 2.8000000000000003. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your an... | 0.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (2(1|(-1sin(3πx - 2) - 1) - 3| + 3) - 1)/(1(1|(-1sin(3πx - 2) - 1) - 3| + 3) - 3) and g(x) = 1|(-3|x + 2| + 2) - 1| - 3 from x = -4.3 to x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 17.0 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1(-2sin(3π(2|x + 2|) + 3) - 3) + 5 and g(x) = 3|(2x^2 - 4x + 3) - 1| - 2 from x = -0.2 to x = 2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 17.3 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2|((1(1sin(1πx)) + 2)/(3(1sin(1πx)) + 3)) - 3| + 1 and g(x) = 3e^(1(-3x^2 + 3x + 3)) + 3 from x = -0.8 to x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.3 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|((-3(1x^2 - 3x + 2))/(-1(1x^2 - 3x + 2) - 2)) - 2| and g(x) = -5(3sin(2πx + 3) + 2)^2 - 2(3sin(2πx + 3) + 2) - 1 between the vertical lines x = -3.7 and x = -3.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \... | 0.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1e^(-1((2(-2|x - 1| + 3) + 3)/(-2(-2|x - 1| + 3) - 2))), g(x) = -4(3cos(1πx - 3) - 1) + 5, x = -2.7, and x = -1.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 15.9 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3e^(1(-1((2x - 2)/(-3x - 1))^2 - 4((2x - 2)/(-3x - 1)) - 5)) + 2 and g(x) = -1|(1|x + 2| - 2) + 1| + 3 between the vertical lines x = -4.3 and x = 0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your a... | 4.0 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-1((2(2sin(3πx - 1) - 3) - 2)/(-2(2sin(3πx - 1) - 3) + 3)) + 1)/(-2((2(2sin(3πx - 1) - 3) - 2)/(-2(2sin(3πx - 1) - 3) + 3)) + 1), g(x) = 4(2|x| - 1)^2 + 1(2|x| - 1) - 2, x = -0.8, and x = -0.0. Round your answer to 1 decimal place.\n\nPrese... | 1.5 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1|((-3(-3cos(3πx) - 2))/(-3(-3cos(3πx) - 2) - 2))| and g(x) = 1sin(2π(-5x - 5) + 3) + 3 from x = -2.4 to x = -2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -3e^(-1((-1(2x^2 - 5x + 2) - 1)/(-2(2x^2 - 5x + 2)))) + 3, g(x) = -3(3cos(1πx - 2) - 1)^2 - 4(3cos(1πx - 2) - 1) + 5, x = 0.9, and x = 1.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 1.4 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1cos(2π(-3(4x^2 - 1x - 4)^2 + 5(4x^2 - 1x - 4) - 5) - 1) + 2, g(x) = -5(-2|x| + 1) - 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}",
"role": "user"
}
] | 0.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 4(-3cos(2π(4x^2 - 4x + 4) - 1) + 1)^2 - 3(-3cos(2π(4x^2 - 4x + 4) - 1) + 1) - 4 and g(x) = 4(-3|x + 3|)^2 + 3(-3|x + 3|) - 2 between the vertical lines x = -3.0 and x = -2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex ... | 1.8 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1sin(1π((-1(-2|x - 2| + 2) + 3)/(-3(-2|x - 2| + 2) - 1)) - 2) + 3 and g(x) = 1sin(2π(-3|x + 3| + 1) - 2) + 3 between the vertical lines x = 0.7 and x = 0.7999999999999999. Round to 1 decimal place.\n\nPresent the answer in LaTex fo... | 0.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 4(2cos(2π(-2x - 3) - 2))^2 + 5(2cos(2π(-2x - 3) - 2)) + 3 and g(x) = 1((-2x + 1)/(3x + 2)) + 3 between the vertical lines x = -3.8 and x = -3.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",... | 3.8 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1|(-5(1x^2 - 2x - 5) - 5) - 3| + 3, g(x) = -4(-2x^2 + 1x - 4) - 2, x = -0.3, and x = 1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11.3 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 4(-2sin(2π(-1x^2 - 1x + 1) - 1))^2 + 4(-2sin(2π(-1x^2 - 1x + 1) - 1)) + 4, g(x) = 3|(4x - 1)|, x = 1.2, and x = 1.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.5 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1sin(1π((3(-1x^2 + 5x - 5) - 2)/(2(-1x^2 + 5x - 5) + 3)) + 2) + 1, g(x) = -1sin(1π((1x)/(1x + 3)) - 2), x = 0.8, and x = 0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 0.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1((1(-3cos(1πx - 3)) - 2)/(-2(-3cos(1πx - 3)) - 3)) + 1 and g(x) = 1|(-5x^2 - 4x - 3) + 2| + 1 from x = -2.7 to x = -1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 22.8 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1cos(1π((-3(3x + 1))/(-1(3x + 1) - 2)) + 2) + 2 and g(x) = 3cos(2π((2x - 3)/(1x)) + 2) + 3 from x = -0.0 to x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1cos(1π(3((-2x + 3)/(1x))^2 + 4((-2x + 3)/(1x)) + 2) - 2) - 2, g(x) = (-1((3x - 2)/(-1x - 3)) + 2)/(2((3x - 2)/(-1x - 3)) + 1), x = 2.5, and x = 3.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your ... | 0.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1|(-1(3sin(2πx + 1) + 2)) - 1| + 3, g(x) = -1(2sin(3πx - 1) + 3)^2 + 5(2sin(3πx - 1) + 3) - 4, x = -3.0, and x = -2.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 1.0 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1|((-2((-2x - 2)/(-3x + 2)) - 3)/(1((-2x - 2)/(-3x + 2)))) - 3| + 1, g(x) = -2sin(2π((3x - 1)/(-3x - 3))) + 3, x = -0.3, and x = -0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 0.5 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-3(-1((3x + 1)/(-1x + 3))^2 + 5((3x + 1)/(-1x + 3)) - 4) - 2)/(1(-1((3x + 1)/(-1x + 3))^2 + 5((3x + 1)/(-1x + 3)) - 4) - 2) and g(x) = -2|(-4x^2 - 5x + 2) - 1| + 1 from x = -0.0 to x = 0.3. Round to 1 decimal place.\n\nPresent the answer in... | 0.3 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2cos(2π(2(4x^2 - 5x - 2) - 4) - 3) + 1 and g(x) = -2(3e^(-1x) - 2) + 5 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}",
"role": "user"
}... | 0.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (2((-3(5x + 2))/(3(5x + 2))) + 2)/(-1((-3(5x + 2))/(3(5x + 2))) - 3) and g(x) = -3(-2x^2 + 4x)^2 - 4(-2x^2 + 4x) between the vertical lines x = -0.3 and x = 0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\box... | 0.3 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (2(-3(1x^2 + 1x - 1)^2 - 5(1x^2 + 1x - 1) + 2))/(2(-3(1x^2 + 1x - 1)^2 - 5(1x^2 + 1x - 1) + 2) - 1) and g(x) = -1cos(1π((3x + 3)/(2x - 1)) + 2) + 1 from x = 0.4 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\b... | 0.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-1((-2(3|x + 3| - 1) + 2)/(2(3|x + 3| - 1) + 2)))/(-2((-2(3|x + 3| - 1) + 2)/(2(3|x + 3| - 1) + 2)) + 3), g(x) = 1(2x) - 3, x = -2.7, and x = 1.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your ans... | 18.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1(-3(-2cos(2πx - 3)) - 5)^2 - 3(-3(-2cos(2πx - 3)) - 5) + 4, g(x) = -1|((-1x - 1)/(3x + 1)) + 3| - 1, x = -2.3, and x = -1.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 23.3 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(-3(-2x^2 + 4x - 3)^2 - 5(-2x^2 + 4x - 3) - 3)| + 1 and g(x) = 2(-2sin(3πx) - 1)^2 - 4(-2sin(3πx) - 1) - 5 between the vertical lines x = 1.0 and x = 1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Yo... | 3.0 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(-2cos(1π(4x - 2) - 1) - 2) - 2 and g(x) = -3sin(1π(-2x) - 2) + 3 between the vertical lines x = 0.7 and x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.6 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-1(-2(-4x + 4)) - 1)/(3(-2(-4x + 4)) + 2), g(x) = 3|(1sin(3πx + 3) + 1) - 1| - 1, x = 2.3, and x = 2.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1sin(2π(1(-1|x - 3| - 2) - 3) - 2) - 3, g(x) = 3cos(2π(-4x - 3) + 3) - 1, x = -3.6, and x = -3.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3(-2|(-1x^2 + 2x) - 2| + 3)^2 + 5(-2|(-1x^2 + 2x) - 2| + 3) + 1, g(x) = (-3(-3|x + 2| + 2) + 1)/(-2(-3|x + 2| + 2)), x = -0.2, and x = 0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 0.9 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3(5(1cos(1πx + 1) - 1)^2 + 3(1cos(1πx + 1) - 1)) + 3, g(x) = -2e^(1(1x + 2)) + 3, x = -4.4, and x = -4.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-2((3(-3x^2 + 5x + 4) - 2)/(-1(-3x^2 + 5x + 4) - 1)) + 3)/(3((3(-3x^2 + 5x + 4) - 2)/(-1(-3x^2 + 5x + 4) - 1)) + 2), g(x) = -1|(-4x + 4) - 1| - 2, x = -0.4, and x = 2.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex f... | 6.6 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3sin(1π(-3((-3x - 1)/(1x + 1))^2 + 4((-3x - 1)/(1x + 1)) - 5) + 1) + 2, g(x) = (-2(-3x^2 + 2x - 5))/(-2(-3x^2 + 2x - 5) - 1), x = -1.5, and x = -1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your a... | 0.2 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -5(-1(-3x^2 - 4x + 2)^2 + 5(-3x^2 - 4x + 2) - 5) - 2, g(x) = -1sin(1π(1|x + 2| - 2) + 1) + 1, x = -1.5, and x = 0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12.3 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (3(5(2x + 1) - 3) - 2)/(2(5(2x + 1) - 3) - 3) and g(x) = 1|(-3sin(1πx + 2) + 3) + 1| - 1 from x = -3.8 to x = -2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3.7 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3(-1|(-4x^2 + 1x) - 3| - 1) + 2)/(-2(-1|(-4x^2 + 1x) - 3| - 1)) and g(x) = 2|(2cos(2πx + 1) - 1) - 3| - 3 between the vertical lines x = 1.9 and x = 2.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{You... | 3.5 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(2|(2sin(3πx - 1) - 3) + 3| - 3) - 1)/(-2(2|(2sin(3πx - 1) - 3) + 3| - 3) + 1) and g(x) = 1(1|x + 2| - 3)^2 - 1(1|x + 2| - 3) - 2 between the vertical lines x = -1.3 and x = -1.1. Round to 1 decimal place.\n\nPresent the answer in... | 1.3 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1|(-2((2x - 3)/(-1x - 3))^2 - 2((2x - 3)/(-1x - 3)) + 2)| + 1 and g(x) = 2sin(2π(1x + 2) + 2) - 2 from x = 0.1 to x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.2 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1(4(2|x - 1| + 2)^2 + 3(2|x - 1| + 2) + 2) - 5, g(x) = 5(-5x + 5)^2 - 1(-5x + 5) + 4, x = 0.4, and x = 1.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(-2e^(2((-1x + 2)/(3x + 1))) + 3) + 3| and g(x) = -3|((-2x + 3)/(-3x + 4))| + 3 between the vertical lines x = 0.5 and x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 0.0 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 3cos(3π((1((3x + 3)/(1x + 3)) - 3)/(2((3x + 3)/(1x + 3)) + 1)) - 2) and g(x) = 3e^(-1(1|x - 3| - 2)) from x = -1.7 to x = -1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(-4(-5x^2 - 3x + 5) + 2) - 1| - 3 and g(x) = (2(1|x - 3| - 3) + 2)/(-1(1|x - 3| - 3) + 2) between the vertical lines x = -1.5 and x = -1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 1.3 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 5(-5(-3cos(2πx - 3) - 2) + 3) + 3, g(x) = -2e^(2((-1x)/(-2x + 1))), x = -1.0, and x = -0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 71.5 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (3(-3cos(3π(1x^2 + 4x + 5) + 1)) - 3)/(-2(-3cos(3π(1x^2 + 4x + 5) + 1)) + 3), g(x) = -3|(1x - 3) - 1| - 3, x = 3.3, and x = 3.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 0.4 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1|(-2sin(2π((-2x + 2)/(3x + 3)) - 2) + 2) + 1| - 1 and g(x) = -1|(2cos(3πx - 2) + 2) + 1| + 1 from x = 3.4 to x = 3.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.4 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1sin(1π(2|((2x + 2)/(-1x + 3)) - 2| - 2) + 2) - 1 and g(x) = 1cos(1π((1x - 3)/(-2x - 2)) - 3) - 2 from x = -0.9 to x = -0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (1(-1(-3x - 5)^2 - 3(-3x - 5) + 4))/(-2(-1(-3x - 5)^2 - 3(-3x - 5) + 4) - 2), g(x) = 2|(-5x + 1) + 3|, x = -2.1, and x = -0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 36.4 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2(3cos(3π(4x + 4) + 1) - 2)^2 + 3, g(x) = 2|(3x^2 + 3x + 2)|, x = -0.4, and x = -0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.4 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|(-1|(-1|x + 3| - 2) - 1| - 2) - 1| + 3 and g(x) = -2|(-4x) - 1| + 1 between the vertical lines x = -2.4 and x = 4.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 85.5 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2sin(3π(-1((-3x - 3)/(-3x - 3))^2 - 1((-3x - 3)/(-3x - 3)) - 5) + 2) and g(x) = 5(4x^2 - 4x - 1)^2 + 5(4x^2 - 4x - 1) - 2 from x = -0.2 to x = 0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 0.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3(1sin(3π(-5x - 2)) - 1)^2 + 5(1sin(3π(-5x - 2)) - 1) + 3 and g(x) = (1(-5x + 4) + 1)/(1(-5x + 4) + 3) from x = 1.7 to x = 1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -3|((1(5x - 2) + 3)/(-2(5x - 2) - 3))|, g(x) = -1((2x - 2)/(-3x)) - 2, x = 0.4, and x = 1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1sin(1π(1|(4x + 4) - 2| - 3) + 1) and g(x) = -3(-3sin(1πx - 1) + 2) - 1 from x = -1.0 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 14.6 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1((-3(-1x^2 + 2x + 1))/(2(-1x^2 + 2x + 1) + 1)) + 3)/(-2((-3(-1x^2 + 2x + 1))/(2(-1x^2 + 2x + 1) + 1)) - 1) and g(x) = (1(1sin(1πx + 3) + 3) - 3)/(3(1sin(1πx + 3) + 3)) between the vertical lines x = -0.5 and x = 2.5. Round to 1 d... | 15.5 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -4((-3((-1x - 1)/(1x + 2)) + 2)/(2((-1x - 1)/(1x + 2)) + 3))^2 + 2 and g(x) = -1|(4x^2 + 1x + 5) + 2| + 1 from x = -2.3 to x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 19.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (3(-5(-3e^(-2x) - 1)^2 + 4(-3e^(-2x) - 1) - 2) + 3)/(-3(-5(-3e^(-2x) - 1)^2 + 4(-3e^(-2x) - 1) - 2) + 2), g(x) = -1(-1|x + 3| + 1)^2 - 5(-1|x + 3| + 1) - 2, x = -4.2, and x = -1.8. Round your answer to 1 decimal place.\n\nPresent the answer ... | 7.9 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(3(-1sin(2πx + 3) - 3) + 3) + 1 and g(x) = 3(1|x - 2| + 1) + 2 between the vertical lines x = -4.9 and x = -4.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -3e^(2(-1|(2x - 4)| + 2)) + 1, g(x) = 1(4x - 1)^2 + 2(4x - 1) + 1, x = -0.2, and x = 0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.3 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(4(-1|x - 2| + 3)^2 + 1(-1|x - 2| + 3) - 5) - 2)/(-3(4(-1|x - 2| + 3)^2 + 1(-1|x - 2| + 3) - 5) - 2) and g(x) = -3((2x + 1)/(-1x - 3)) between the vertical lines x = -0.4 and x = 0.0. Round to 1 decimal place.\n\nPresent the answ... | 2.2 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 4(-3e^(2((2x + 2)/(1x + 3))) + 1) - 4, g(x) = 3sin(3π((1x - 3)/(-2x - 3)) - 2) + 2, x = -3.0, and x = -2.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.0 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1|(1(2sin(2πx + 1) - 3) - 4) - 2| - 3 and g(x) = (2(2|x + 1| + 3))/(1(2|x + 1| + 3) - 2) from x = -1.1 to x = -0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.3 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|((1(-2x^2 + 4) + 2)/(2(-2x^2 + 4) + 1)) - 1| - 3 and g(x) = -2(-3|x - 3| - 2) + 2 between the vertical lines x = -1.5 and x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 85.6 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(1(-2|x - 1| + 3) - 1)^2 - 5(1(-2|x - 1| + 3) - 1) - 3 and g(x) = 3cos(2π((3x - 2)/(3x))) + 1 between the vertical lines x = -0.1 and x = 2.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",... | 19.5 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1cos(3π((-2((-1x + 1)/(2x - 1)) + 2)/(1((-1x + 1)/(2x - 1)) + 3)) - 2) - 3 and g(x) = -1sin(3π(-3|x - 1| - 3) - 3) - 3 between the vertical lines x = 0.3 and x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format:... | 0.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3sin(3π(-1|(-1x^2 - 3x - 2)| + 2) + 1) + 1 and g(x) = -1e^(-1(3|x - 2|)) - 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}",
"role": "user"... | 0.3 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (3(-1|((-2x - 2)/(2x - 3)) - 2| + 1) - 1)/(-3(-1|((-2x - 2)/(2x - 3)) - 2| + 1)) and g(x) = 1cos(3π(-2x - 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}",
"role": "u... | 0.0 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(1|(-2|x + 3| + 3) + 3| + 1))/(-3(1|(-2|x + 3| + 3) + 3| + 1)) and g(x) = 1|(-5x - 4) + 1| - 1 between the vertical lines x = -0.9 and x = -0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer... | 0.5 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|(3|(2|x + 1| - 1) - 3| - 1) + 3| - 2 and g(x) = (-3(1x^2 - 1x - 5) - 3)/(2(1x^2 - 1x - 5) - 1) between the vertical lines x = -1.8 and x = 2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"... | 38.7 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(-3|((-2x + 1)/(2x)) + 2| - 3)^2 + 3(-3|((-2x + 1)/(2x)) + 2| - 3) + 4 and g(x) = (2(2sin(1πx - 2) - 1) + 1)/(-3(2sin(1πx - 2) - 1) + 1) between the vertical lines x = 1.4 and x = 2.9. Round to 1 decimal place.\n\nPresent the answ... | 92.4 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -3((-2(3e^(2x)) + 3)/(-1(3e^(2x)) - 1)) + 3, g(x) = (-3((-2x - 1)/(1x + 1)) - 1)/(-1((-2x - 1)/(1x + 1)) - 3), x = 1.0, and x = 1.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 0.0 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 5(-1|((-1x + 1)/(-3x + 1))| + 2)^2 - 2(-1|((-1x + 1)/(-3x + 1))| + 2) + 4, g(x) = 3((-1x + 1)/(3x + 2))^2 - 5((-1x + 1)/(3x + 2)) - 3, x = -1.1, and x = -0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\box... | -11.6 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2((-2(-3x - 5) - 3)/(1(-3x - 5) + 2)) + 5 and g(x) = 4((-1x + 1)/(2x - 1)) 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}",
"role": "user"
... | 21.8 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1(-2|((2x + 3)/(-2x - 2)) - 2| + 2) + 4 and g(x) = -1(2x^2 + 1x + 2)^2 + 3(2x^2 + 1x + 2) - 2 from x = -1.1 to x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 54.8 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1|((-2(-3x - 3))/(2(-3x - 3) + 3)) + 3| - 3, g(x) = 3((3x - 1)/(3x + 3))^2 + 5((3x - 1)/(3x + 3)) + 5, x = -0.6, and x = -0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 20.0 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|((3(-1e^(2x) - 3) - 2)/(-3(-1e^(2x) - 3) + 2)) + 3| - 2 and g(x) = -4(2e^(-2x) - 2)^2 + 5(2e^(-2x) - 2) + 5 between the vertical lines x = -0.3 and x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{... | 1.3 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -5(-5(1x + 4) - 4) + 2, g(x) = (-2(3sin(1πx + 1) + 1))/(1(3sin(1πx + 1) + 1) + 1), x = -3.1, and x = -2.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 35.0 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 5(-4(-3cos(2πx) - 2) - 3)^2 - 2(-4(-3cos(2πx) - 2) - 3) - 4 and g(x) = -2|(-1x^2 + 5x) + 1| - 2 between the vertical lines x = -0.3 and x = -0.19999999999999998. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\box... | 13.7 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-3(3(3sin(1πx - 2)) + 2) - 1)/(2(3(3sin(1πx - 2)) + 2) + 3), g(x) = 2|((2x - 3)/(1x + 2)) - 1|, x = -4.2, and x = -3.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 8.3 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 2(-1(-1e^(1x) + 1)^2 - 1(-1e^(1x) + 1) + 1) + 4, g(x) = 2|((3x - 2)/(3x + 3)) + 1| + 3, x = -0.4, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.2 | MATH |
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