messages listlengths 1 1 | ground_truth stringlengths 3 8 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2(-2e^(2(5(-3|x - 3| + 3) + 1)) - 3)^2 and g(x) = -2(-2|(-3cos(3πx - 3) - 3) + 2| - 3) - 4 from x = -3.7 to x = -3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5.3 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1(1((1x + 1)/(-3x)))^2 - 5(1((1x + 1)/(-3x))) + 2 and g(x) = 3|(-3cos(2πx + 3) - 1) - 3| - 3 from x = -3.8 to x = -3.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6.3 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(-2|(-1x^2 + 2x + 3) + 2| - 3) - 1)/(-1(-2|(-1x^2 + 2x + 3) + 2| - 3) - 2) and g(x) = -2e^(-1(1x^2 + 5x + 3)) + 3 between the vertical lines x = -4.0 and x = -1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \... | 67.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1((3(-1(-1|x - 3| + 2)^2 - 1(-1|x - 3| + 2)) - 2)/(3(-1(-1|x - 3| + 2)^2 - 1(-1|x - 3| + 2)) + 3)) + 1 and g(x) = 1(-3|(1x^2 + 2x - 5)| - 1) - 5 between the vertical lines x = -0.6 and x = 1.5. Round to 1 decimal place.\n\nPresent t... | 33.5 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (1(-3(1sin(2π(-5x + 1) + 3))^2 + 4(1sin(2π(-5x + 1) + 3)) + 5) + 3)/(2(-3(1sin(2π(-5x + 1) + 3))^2 + 4(1sin(2π(-5x + 1) + 3)) + 5)) and g(x) = 3(3((3x - 3)/(1x))^2 - 1((3x - 3)/(1x)) - 1) from x = 0.8 to x = 0.9. Round to 1 decimal place.\n\... | 0.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3|(-1sin(3π((1x + 3)/(1x + 2))) - 1) - 2| - 3 and g(x) = -5((1x - 3)/(-1x + 3))^2 + 4((1x - 3)/(-1x + 3)) 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"
... | 0.3 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 5((-1(-1sin(2πx - 3)) - 2)/(-1(-1sin(2πx - 3)) + 2))^2 - 5((-1(-1sin(2πx - 3)) - 2)/(-1(-1sin(2πx - 3)) + 2)) - 3 and g(x) = 1sin(3π(1x - 5) + 3) + 3 between the vertical lines x = 2.9 and x = 3.5. Round to 1 decimal place.\n\nPrese... | 14.4 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-2(-2sin(1π(-1|x + 1| + 2))) + 2)/(-2(-2sin(1π(-1|x + 1| + 2))) - 1), g(x) = -3|(-1x + 3) - 1|, x = 4.0, and x = 4.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 12.7 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1(2((1(2sin(2πx - 3) - 2) + 3)/(3(2sin(2πx - 3) - 2) + 1))^2 + 4((1(2sin(2πx - 3) - 2) + 3)/(3(2sin(2πx - 3) - 2) + 1)) - 3) + 1 and g(x) = -3cos(2π(3(3|x + 1| - 2) + 2) - 1) + 3 from x = -1.7 to x = -1.6. Round to 1 decimal place.\n\nPrese... | 0.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 5((-2(-1|x - 3| + 1) - 3)/(2(-1|x - 3| + 1) + 1))^2 - 4((-2(-1|x - 3| + 1) - 3)/(2(-1|x - 3| + 1) + 1)) - 4 and g(x) = 1|(-4x - 2)| - 2 between the vertical lines x = -0.3 and x = 1.1. Round to 1 decimal place.\n\nPresent the answer... | 6.6 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-2(3cos(1π(-4x + 2) + 3) - 2) - 3)/(3(3cos(1π(-4x + 2) + 3) - 2) - 1) and g(x) = (3(-1cos(2πx - 1) - 2))/(2(-1cos(2πx - 1) - 2) + 3) from x = -3.8 to x = -3.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your an... | 3.0 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1|(-1(4x^2 + 1x + 3)) - 3| + 3, g(x) = -3sin(3π(-5x + 3)) - 2, x = -0.5, and x = -0.4. 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) = (-1(4(1|(-2x + 1) + 3| + 1)^2 + 1(1|(-2x + 1) + 3| + 1)) + 2)/(-2(4(1|(-2x + 1) + 3| + 1)^2 + 1(1|(-2x + 1) + 3| + 1)) + 1), g(x) = 1|(2cos(3π((1x - 2)/(1x - 3)))) + 1| - 1, x = 2.4, and x = 2.5. Round your answer to 1 decimal place.\n\nPres... | 0.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (2(3(2(-2|x + 1| + 3)^2 + 3(-2|x + 1| + 3) - 3) - 5) + 3)/(1(3(2(-2|x + 1| + 3)^2 + 3(-2|x + 1| + 3) - 3) - 5) - 3), g(x) = (3(-1(1x + 1)^2 - 1(1x + 1) - 2) + 2)/(1(-1(1x + 1)^2 - 1(1x + 1) - 2) + 1), x = -1.9, and x = -0.2. Round your answe... | 2.6 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 3sin(1π(-1(1x^2 - 5x - 1) - 2) + 3) - 3 and g(x) = 2|(2x^2 - 1x - 3) + 1| - 3 from x = -1.0 to x = -0.9. 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) = (2(2cos(2π(1x^2 + 4x + 5) + 2) + 1))/(2(2cos(2π(1x^2 + 4x + 5) + 2) + 1) + 3), g(x) = (3(1e^(1x) + 2) - 3)/(-1(1e^(1x) + 2) - 3), x = 1.4, and x = 1.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your... | 0.2 | 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) + 4) + 2)/(3(-2(3|x + 3| + 1)^2 + 2(3|x + 3| + 1) + 4) - 2), g(x) = (-3(1sin(2πx - 2) - 1) - 2)/(-2(1sin(2πx - 2) - 1) - 3), x = -0.6, and x = -0.2. Round your answer to 1 decimal place.\n\nPresent th... | 0.3 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1(1|(-2e^(-1(-1x^2 - 2x - 2)) - 1) - 2| - 3) - 3 and g(x) = (2(-3sin(2π(1x + 4) - 3) + 3))/(3(-3sin(2π(1x + 4) - 3) + 3) - 1) from x = -0.4 to x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",... | 2.8 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1((-2(-4(3|x + 2| + 3)^2 - 1(3|x + 2| + 3) + 2) + 3)/(2(-4(3|x + 2| + 3)^2 - 1(3|x + 2| + 3) + 2) - 3)) + 1 and g(x) = 3|(-2e^(-2((-1x - 1)/(-1x - 2))) + 1) + 2| - 3 from x = -1.3 to x = -0.8. Round to 1 decimal place.\n\nPresent the answer... | 1.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 3e^(1(-2(2x - 5)^2 - 2)) - 2 and g(x) = 2cos(1π(1x + 2) + 3) - 1 from x = 2.4 to x = 3.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.3 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(1sin(1π(-2|(-3x^2 + 3) - 1| - 3) + 3) + 2) + 5 and g(x) = -1((2(3|x - 1| - 2))/(-1(3|x - 1| - 2) + 3)) + 4 between the vertical lines x = 4.6 and x = 4.699999999999999. Round to 1 decimal place.\n\nPresent the answer in LaTex form... | 0.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1cos(2π(-5((3(2|x - 3|) + 3)/(-1(2|x - 3|) + 2)) - 2) + 1) - 1 and g(x) = 2(1cos(1π(-3x - 5) - 3) - 2)^2 + 1(1cos(1π(-3x - 5) - 3) - 2) - 5 between the vertical lines x = 3.9 and x = 4.1. Round to 1 decimal place.\n\nPresent the an... | 0.5 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-1(-3sin(1π(-5x^2 - 5x - 3) + 1)) - 2)/(3(-3sin(1π(-5x^2 - 5x - 3) + 1)) + 3), g(x) = (-2(-3|x - 2|))/(-2(-3|x - 2|) - 1), x = 4.1, and x = 4.199999999999999. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\bo... | 0.2 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -3|(1((-1(-2e^(-1x) - 1) + 1)/(2(-2e^(-1x) - 1) + 2)) + 2) - 1| - 3, g(x) = (-2(-3(-3|x + 1| + 2)^2 - 1(-3|x + 1| + 2) + 5) - 1)/(-3(-3(-3|x + 1| + 2)^2 - 1(-3|x + 1| + 2) + 5) - 2), x = -1.3, and x = -0.7. Round your answer to 1 decimal pla... | 2.8 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(4(-5x^2 - 5x + 3) + 2) - 1)/(-2(4(-5x^2 - 5x + 3) + 2) - 1) and g(x) = -3|(1sin(1πx + 1) - 2) + 1| + 3 between the vertical lines x = -1.3 and x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{You... | 1.5 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-3(1(-3|x - 3| - 3) + 1) + 1)/(1(1(-3|x - 3| - 3) + 1) + 3), g(x) = -3sin(3π(1x^2 - 4x - 2) - 3) - 2, x = -2.7, and x = -2.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 0.2 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 5(-2|((3(3cos(3πx - 3)) + 1)/(1(3cos(3πx - 3)) - 2)) - 2| + 3), g(x) = -1|(3sin(3π(-4x) - 2) - 1) + 1| - 1, x = 3.2, and x = 3.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 3.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2cos(1π((2(1x + 3) - 2)/(-1(1x + 3) + 3))) - 3 and g(x) = -2sin(3π(-3x + 5) - 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}",
"rol... | 0.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(-3(1(2e^(-2x) + 1) - 3)^2 + 3(1(2e^(-2x) + 1) - 3) - 1) + 2| + 3 and g(x) = (3(3cos(1π(-1x^2 + 2x - 1) - 3) - 1) + 3)/(1(3cos(1π(-1x^2 + 2x - 1) - 3) - 1) + 2) between the vertical lines x = 3.5 and x = 3.8. Round to 1 decimal p... | 11.4 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(-2((3(1e^(-1x) + 2) + 2)/(2(1e^(-1x) + 2) - 3))^2 + 4((3(1e^(-1x) + 2) + 2)/(2(1e^(-1x) + 2) - 3)) - 5) + 5 and g(x) = 2|(-2((-2x + 1)/(-2x)) - 1)| - 2 between the vertical lines x = -0.0 and x = 0.1. Round to 1 decimal place.\n\... | 42.8 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2|(5((1(-5x^2 - 1x - 4))/(-1(-5x^2 - 1x - 4) - 1)) + 1) - 1| and g(x) = (-2(-5(3cos(2πx + 1)) + 5) - 1)/(1(-5(3cos(2πx + 1)) + 5) + 3) from x = -2.0 to x = -1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your a... | 9.4 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1(3(-2|((2x - 3)/(-3x - 1)) - 1|)^2 + 2(-2|((2x - 3)/(-3x - 1)) - 1|) - 4) + 1 and g(x) = (-3(-1(-2|x + 1|)^2 - 2(-2|x + 1|) + 2) - 3)/(-2(-1(-2|x + 1|)^2 - 2(-2|x + 1|) + 2) - 1) from x = 0.2 to x = 0.4. Round to 1 decimal place.\n\nPresen... | 0.5 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1e^(1(2|(-2x - 4) + 3| + 2)) + 1 and g(x) = 5(-2e^(1x))^2 - 5(-2e^(1x)) - 4 between the vertical lines x = -0.5 and x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 0.0 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -3(1sin(3π((-2(-1|x - 3| - 2))/(-2(-1|x - 3| - 2) - 3)) + 2) + 2) - 1, g(x) = -5(3cos(3π(-1x) + 1) + 2)^2 + 4(3cos(3π(-1x) + 1) + 2) - 2, x = -0.7, and x = -0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\... | 18.9 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(-3|(-2(-1x^2 - 1x - 1) + 4) + 1| + 1) - 3)/(2(-3|(-2(-1x^2 - 1x - 1) + 4) + 1| + 1) + 1) and g(x) = -3e^(-1(-1(2|x| - 1) + 1)) between the vertical lines x = -0.4 and x = 0.4. Round to 1 decimal place.\n\nPresent the answer in L... | 0.3 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3|(5((-3x - 3)/(-1x + 2))^2 - 3((-3x - 3)/(-1x + 2)) + 5) - 3| + 3 and g(x) = -2(-3e^(2x) - 3)^2 + 3 from x = 1.8 to x = 2.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -33227.5 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -4(-4(-2cos(3πx - 2) + 2)^2 + 5(-2cos(3πx - 2) + 2) + 2) - 1, g(x) = (-1(1e^(2x)) + 3)/(-1(1e^(2x))), x = 0.1, and x = 0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 3.5 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1sin(3π(3((-2x + 3)/(3x - 1))^2 - 3) - 3) + 1, g(x) = 1(3cos(3πx + 3) + 3)^2 - 3(3cos(3πx + 3) + 3) - 1, x = -2.8, and x = -2.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 1.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2cos(1π(-3(-3|((-2x - 1)/(-1x + 2)) - 2| - 3) - 4) + 3) + 2 and g(x) = 2sin(3π(-1|(3x - 2) + 2| - 1) + 2) + 1 between the vertical lines x = 1.5 and x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{... | 0.2 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3cos(2π(-3((-2x - 3)/(-3x))^2 - 1((-2x - 3)/(-3x)) + 1) - 3) + 3, g(x) = (-3(3|x - 3| - 2) + 1)/(-1(3|x - 3| - 2) + 2), x = -0.4, and x = -0.30000000000000004. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\bo... | 0.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1((2(-4(-2|x - 2| + 2)^2 + 3(-2|x - 2| + 2) + 1) + 3)/(2(-4(-2|x - 2| + 2)^2 + 3(-2|x - 2| + 2) + 1) - 1)) + 1 and g(x) = -4(2((-2x - 1)/(3x + 1))^2 + 3((-2x - 1)/(3x + 1)) - 2) + 3 from x = 0.9 to x = 1.5. Round to 1 decimal place.\n\nPres... | 21.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1cos(1π(-3(2|x + 3| - 2) - 5) + 3) - 1 and g(x) = 4((2x)/(-2x + 1)) + 5 between the vertical lines x = 1.6 and x = 1.7. 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) = -1(1((-3x + 2)/(2x - 3))^2 - 1((-3x + 2)/(2x - 3))) + 1 and g(x) = -4(-2cos(2πx - 2) + 3) - 1 between the vertical lines x = 2.5 and x = 3.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 5.9 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(-4(2|x + 2| + 3)^2 + 2(2|x + 2| + 3) + 3) + 3)/(1(-4(2|x + 2| + 3)^2 + 2(2|x + 2| + 3) + 3) - 3) and g(x) = -3(-3e^(2x) + 1)^2 - 5(-3e^(2x) + 1) between the vertical lines x = -0.3 and x = -0.2. Round to 1 decimal place.\n\nPrese... | 0.0 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-2(2|(-1e^(2x) - 1) - 2| + 1) - 1)/(2(2|(-1e^(2x) - 1) - 2| + 1) + 2) and g(x) = 2(3cos(2πx) - 2)^2 - 3(3cos(2πx) - 2) - 2 from x = -3.2 to x = -2.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 0.7 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2|((2(2(3x - 4)^2 + 1(3x - 4) - 3) + 3)/(3(2(3x - 4)^2 + 1(3x - 4) - 3) - 2)) - 2| + 1, g(x) = (2(5(3sin(3πx) + 1)^2 - 1(3sin(3πx) + 1) - 5) + 3)/(1(5(3sin(3πx) + 1)^2 - 1(3sin(3πx) + 1) - 5) - 3), x = -0.7, and x = -0.3. Round your answer ... | 2.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -2|(1(5x + 3)^2 + 4(5x + 3) + 3) - 2| - 2 and g(x) = (-2(-3x^2 + 2x + 3))/(1(-3x^2 + 2x + 3)) from x = -1.4 to x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.9 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|((-1(-1(-2x^2 - 1x + 1) - 2) - 2)/(-1(-1(-2x^2 - 1x + 1) - 2) - 1)) + 2| - 1 and g(x) = (3(-5(3|x + 1| - 3)^2 + 4(3|x + 1| - 3)) + 1)/(-2(-5(3|x + 1| - 3)^2 + 4(3|x + 1| - 3)) - 2) between the vertical lines x = -1.9 and x = -0.1.... | 21.6 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1(-2((1x - 3)/(2x - 1))^2 - 4((1x - 3)/(2x - 1)) - 3) + 3, g(x) = (-2(3x + 3) + 3)/(3(3x + 3) + 3), x = -1.4, and x = 1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 21.7 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1((1(-2x - 2) - 3)/(1(-2x - 2) - 2))^2 + 1((1(-2x - 2) - 3)/(1(-2x - 2) - 2)) - 5, g(x) = 3|((-3x + 2)/(-2x - 2)) - 1|, x = -2.1, and x = -1.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}... | -6.4 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2sin(2π(1(2(-3|x - 1| + 1) + 5)^2 - 4(2(-3|x - 1| + 1) + 5) - 5) - 1) + 3 and g(x) = (-2(3(-2x + 2)^2 + 4(-2x + 2) + 4) - 2)/(-1(3(-2x + 2)^2 + 4(-2x + 2) + 4) - 3) from x = 4.5 to x = 4.6. Round to 1 decimal place.\n\nPresent the answer in ... | 0.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(2(1((-2x - 3)/(3x)) - 4)^2 - 4(1((-2x - 3)/(3x)) - 4) - 3) + 1| - 3 and g(x) = 1(-1|(2sin(3πx - 2) - 3) - 3| + 2)^2 + 4(-1|(2sin(3πx - 2) - 3) - 3| + 2) between the vertical lines x = -0.2 and x = -0.1. Round to 1 decimal place.... | 1.5 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2((-1(2|(5x + 2) - 1| - 3) + 3)/(-1(2|(5x + 2) - 1| - 3) - 2))^2 - 1((-1(2|(5x + 2) - 1| - 3) + 3)/(-1(2|(5x + 2) - 1| - 3) - 2)) - 1 and g(x) = 2(1|(-2x^2 - 2x)| - 3) - 2 between the vertical lines x = 0.1 and x = 0.8. Round to 1 ... | 2.7 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1|(1(-3sin(3π((3x + 1)/(-1x - 2))) + 1)^2 + 1(-3sin(3π((3x + 1)/(-1x - 2))) + 1)) - 1| - 2 and g(x) = -1(-3|((-2x - 3)/(2x - 1))| + 2) - 5 from x = -2.3 to x = -2.1999999999999997. Round to 1 decimal place.\n\nPresent the answer in LaTex fo... | 0.5 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1cos(2π((1(1|(4x + 5) - 1| - 2) + 2)/(3(1|(4x + 5) - 1| - 2) + 2)) - 1) - 2, g(x) = (2(1(-4x - 2)^2 + 3(-4x - 2)) + 1)/(2(1(-4x - 2)^2 + 3(-4x - 2)) - 3), x = -0.6, and x = 0.3. Round your answer to 1 decimal place.\n\nPresent the answer in... | 1.5 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(-1|((1(2x + 1))/(-2(2x + 1) + 3)) - 3| + 2)^2 - 3(-1|((1(2x + 1))/(-2(2x + 1) + 3)) - 3| + 2) - 3 and g(x) = 1cos(2π(-4(1x^2 + 2x + 5) - 5) - 1) - 2 between the vertical lines x = -0.0 and x = 0.2. Round to 1 decimal place.\n\nPre... | 0.5 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1|(-1sin(2π((-3(4x^2 + 4x - 3) + 2)/(1(4x^2 + 4x - 3)))) - 2) + 3| - 2 and g(x) = 4(3|(2x^2 + 5x - 1) - 1| - 1) - 2 from x = 0.4 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 0.3 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2sin(3π(5((-3x)/(-3x - 3))^2) + 3) - 3 and g(x) = -2|((-1x - 2)/(-2x + 1))| - 3 from x = -2.3 to x = -2.1999999999999997. 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(2sin(1π(1|x - 3| + 1) + 2) - 3) + 4 and g(x) = 3|(5x^2 + 4x + 5) - 2| - 2 between the vertical lines x = -1.1 and x = -0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 5.3 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(4((-2(-2|x - 1| + 2) + 2)/(-1(-2|x - 1| + 2) - 3))^2 - 1((-2(-2|x - 1| + 2) + 2)/(-1(-2|x - 1| + 2) - 3)) - 3) - 1 and g(x) = (3(5(-2|x - 3| - 1)^2 + 4(-2|x - 3| - 1) + 1) + 3)/(-1(5(-2|x - 3| - 1)^2 + 4(-2|x - 3| - 1) + 1) - 1) ... | 9.7 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1cos(2π(4(2|x + 2| + 3) + 4) + 1) and g(x) = (-1(-3|x + 3| - 1) + 3)/(-2(-3|x + 3| - 1) + 1) from x = 0.2 to x = 0.3. 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) = -4(1sin(2π((2x - 1)/(-3x + 4)) + 3) - 1)^2 - 4(1sin(2π((2x - 1)/(-3x + 4)) + 3) - 1) - 1 and g(x) = (-2(1|x - 2| + 3) + 1)/(1(1|x - 2| + 3)) from x = 1.5 to x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Yo... | 0.3 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 3|(3e^(1(3(1x^2 - 3x - 1) + 2)) + 3) - 3| + 1 and g(x) = 4(-2e^(-2(2x - 4)) + 1)^2 - 3(-2e^(-2(2x - 4)) + 1) + 1 from x = 2.6 to x = 2.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 0.0 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2(-2cos(1π(5x + 2)) + 3)^2 - 2(-2cos(1π(5x + 2)) + 3) + 4 and g(x) = 1(-1|x + 1| - 3)^2 + 5(-1|x + 1| - 3) - 4 from x = 2.9 to x = 3.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 4.5 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (1(4(-4(3|x + 2| + 2)^2 - 3(3|x + 2| + 2) - 5) - 2) + 2)/(1(4(-4(3|x + 2| + 2)^2 - 3(3|x + 2| + 2) - 5) - 2) + 3), g(x) = 1|(-3(1x^2 - 5x - 2) - 4)| - 2, x = 0.1, and x = 4.9. Round your answer to 1 decimal place.\n\nPresent the answer in La... | 57.6 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2(1e^(-1(5x - 5)) + 3)^2 - 4(1e^(-1(5x - 5)) + 3) - 5 and g(x) = -2cos(1π(5x - 3) + 2) from x = 3.4 to x = 3.5. 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) = -1((-2(2(1|x - 2| - 3)^2 + 1(1|x - 2| - 3) - 1) + 2)/(-3(2(1|x - 2| - 3)^2 + 1(1|x - 2| - 3) - 1) - 1)) + 2 and g(x) = 2sin(2π(3((2x - 1)/(1x + 2))^2 + 4((2x - 1)/(1x + 2)) - 2) + 3) + 3 between the vertical lines x = -4.0 and x = -... | 0.2 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1((-3(-2e^(-1(2|x - 1| - 1)) - 1) - 1)/(3(-2e^(-1(2|x - 1| - 1)) - 1) + 2))^2 + 2((-3(-2e^(-1(2|x - 1| - 1)) - 1) - 1)/(3(-2e^(-1(2|x - 1| - 1)) - 1) + 2)) - 3, g(x) = 3(-2|((3x)/(3x + 1)) - 3| + 1)^2 + 2(-2|((3x)/(3x + 1)) - 3| + 1) - 5, x ... | 0.9 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2(2((3(3|x + 3| - 1) - 1)/(2(3|x + 3| - 1) - 1))^2 + 1((3(3|x + 3| - 1) - 1)/(2(3|x + 3| - 1) - 1)) - 4) + 5, g(x) = 2(2|(-5x + 4) - 1| - 3)^2 - 2(2|(-5x + 4) - 1| - 3) - 4, x = 0.8, and x = 1.1. Round your answer to 1 decimal place.\n\nPre... | 1.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3|((3(-3x^2 - 5x - 3) + 1)/(2(-3x^2 - 5x - 3) + 3)) - 2| - 2 and g(x) = 2|((-3x + 3)/(3x + 2)) + 1| + 1 between the vertical lines x = -1.5 and x = -1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your ... | 18.3 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3(-2|(-1(4x^2 + 5x - 1) - 3)|) + 3)/(1(-2|(-1(4x^2 + 5x - 1) - 3)|) + 3) and g(x) = 3sin(1π(-5((-3x - 2)/(1x + 3))^2 + 4((-3x - 2)/(1x + 3)) + 3) + 1) + 3 between the vertical lines x = -0.6 and x = -0.5. Round to 1 decimal place.... | 0.2 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2|(1(4((-3x - 2)/(3x + 3))^2 - 2((-3x - 2)/(3x + 3)) - 5) - 5) + 1| - 3, g(x) = -4(4(-1|x - 1| + 1)^2 + 5(-1|x - 1| + 1) - 4) - 2, x = 0.8, and x = 1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Yo... | 2.0 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-3(2(2|x + 2| - 1) - 2))/(-3(2(2|x + 2| - 1) - 2) + 2), g(x) = 2|(-2e^(2x) - 2) - 3| + 3, x = -3.2, and x = -0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 41.6 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 3sin(3π(-5(-3x - 3)^2 + 2(-3x - 3) + 5) + 1) - 2 and g(x) = 1((1x + 3)/(-2x + 1)) + 5 from x = 0.7 to x = 0.7999999999999999. 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) = 1(4(-2cos(3πx - 3) - 1) - 1)^2 - 2(4(-2cos(3πx - 3) - 1) - 1) - 3, g(x) = 3((-1x - 3)/(-2x + 3)) - 4, x = 1.6, and x = 1.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 22.7 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3sin(1π(-2((2x)/(-2x))^2 + 1((2x)/(-2x)) - 3) + 1) - 1 and g(x) = -2cos(2π(-2x - 5) - 3) - 2 between the vertical lines x = -2.7 and x = -2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 0.8 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2|((-1(-1x + 2) - 3)/(1(-1x + 2))) + 3| + 2, g(x) = 1e^(1(-3x - 1)) - 2, x = -0.6, and x = 1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4.4 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (2(5(3|x - 1| - 1) + 1) + 3)/(-3(5(3|x - 1| - 1) + 1) + 4), g(x) = -1(-2x + 4)^2 + 2(-2x + 4) - 1, x = 0.6, and x = 2.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 4.5 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|(1e^(-1(-1x + 4))) + 3| - 2 and g(x) = 5(-2x^2 - 4x) between the vertical lines x = -2.4 and x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40.6 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 2|((-3(4(-2sin(1πx - 2) - 2) - 4) - 3)/(2(4(-2sin(1πx - 2) - 2) - 4) + 3)) - 1| - 2, g(x) = 5((3(3x - 3) - 1)/(-1(3x - 3) - 3))^2 + 2((3(3x - 3) - 1)/(-1(3x - 3) - 3)) - 3, x = 0.8, and x = 2.0. Round your answer to 1 decimal place.\n\nPrese... | 4.6 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -4((1(1e^(1(1|x - 1| + 2)) - 2))/(-1(1e^(1(1|x - 1| + 2)) - 2) - 1)) - 4, g(x) = (1(4(-3x^2 + 1x - 3) + 5) + 2)/(-2(4(-3x^2 + 1x - 3) + 5)), x = 0.6, and x = 1.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \... | 0.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1e^(-2(2|(-5x - 2) - 3| + 3)) + 1 and g(x) = -3sin(2π(4x^2 + 3x + 4) - 1) - 1 from x = 0.4 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (2(-3(1|x| - 2)^2 + 3) + 2)/(1(-3(1|x| - 2)^2 + 3) + 3) and g(x) = -1(-2e^(1x) + 3)^2 - 4(-2e^(1x) + 3) from x = -3.4 to x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 50.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-2(-4(-3|x| - 1)^2 - 4(-3|x| - 1) - 2) + 3)/(1(-4(-3|x| - 1)^2 - 4(-3|x| - 1) - 2) - 3) and g(x) = (-3(-1|x - 3| - 1) + 3)/(1(-1|x - 3| - 1) - 3) from x = 1.2 to x = 5.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\bo... | 0.8 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|(2cos(2π(5x^2 - 5x + 3) - 1) + 1)| - 2 and g(x) = -2(-2sin(1πx) - 3)^2 - 5(-2sin(1πx) - 3) + 4 between the vertical lines x = 1.0 and x = 2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",... | 6.5 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -3(3|((1x - 3)/(-3x + 2)) - 3| - 3)^2 - 4(3|((1x - 3)/(-3x + 2)) - 3| - 3) + 2, g(x) = -4(-1x + 3)^2 - 2(-1x + 3) + 4, x = 0.8, and x = 1.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 4.5 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -4((2(-3cos(2πx + 2) + 1) - 1)/(2(-3cos(2πx + 2) + 1) + 3)) - 3 and g(x) = 3|((-2x - 3)/(1x - 2)) + 2| - 1 from x = 1.6 to x = 1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 30.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(-5(2|x + 1| + 1) + 5) + 1)/(3(-5(2|x + 1| + 1) + 5)) and g(x) = -3((-1x + 1)/(2x - 1)) - 5 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}",... | 0.9 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1(-5(-2e^(-2x) + 2) - 2)^2 - 2(-5(-2e^(-2x) + 2) - 2) - 5, g(x) = 4(-1cos(3πx - 1) + 3) - 5, x = -0.3, and x = 0.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3.0 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (1(-1cos(1π(2|(-5x^2 + 5) + 1| + 1)) + 2) - 1)/(1(-1cos(1π(2|(-5x^2 + 5) + 1| + 1)) + 2)) and g(x) = (3(4(2|x + 2| - 3)))/(2(4(2|x + 2| - 3)) + 2) from x = -3.5 to x = -3.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\... | 0.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 5(-1|(-4x^2 - 1) + 3| + 2) - 2 and g(x) = -4(1|x + 1| - 2)^2 - 4(1|x + 1| - 2) 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}",
"role": "use... | 0.9 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3(3|(1e^(-2x) - 2) - 3| + 2)^2 - 3(3|(1e^(-2x) - 2) - 3| + 2) - 2, g(x) = 2|((1x + 3)/(2x + 2)) - 2| - 1, x = -1.0, and x = -0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 46.5 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-2(3(1|(-2sin(1πx)) - 2| + 2)^2 + 4(1|(-2sin(1πx)) - 2| + 2)) + 3)/(-3(3(1|(-2sin(1πx)) - 2| + 2)^2 + 4(1|(-2sin(1πx)) - 2| + 2))) and g(x) = 2sin(3π(1|(1x^2 + 3x) + 1| + 2) - 3) + 1 from x = 3.7 to x = 3.8000000000000003. Round to 1 decima... | 0.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2((-1(-2|x + 2| + 3) + 2)/(1(-2|x + 2| + 3) + 2))^2 - 3((-1(-2|x + 2| + 3) + 2)/(1(-2|x + 2| + 3) + 2)) + 1, g(x) = -2cos(3π((3x + 2)/(-1x - 3)) - 2) + 3, x = -2.3, and x = -2.1999999999999997. Round your answer to 1 decimal place.\n\nPrese... | 0.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -2|(1(-5x^2 - 4x - 2) + 5) + 2| - 3 and g(x) = 1(1|x - 2| - 1)^2 - 5(1|x - 2| - 1) + 1 from x = -1.6 to x = -1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1((1(-2x + 5) + 2)/(-1(-2x + 5) - 3))^2 + 5((1(-2x + 5) + 2)/(-1(-2x + 5) - 3)) + 2 and g(x) = -2e^(-1(5x^2 + 5x - 4)) + 1 from x = 0.4 to x = 3.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 8.5 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-1(2|(-3(3x + 4)^2 - 4(3x + 4) + 2) - 1| - 2) - 2)/(-2(2|(-3(3x + 4)^2 - 4(3x + 4) + 2) - 1| - 2) + 3) and g(x) = 1|(-4((1x + 3)/(3x + 2)) + 3) - 2| from x = -2.0 to x = -1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format:... | 3.4 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -5(2|((-1x - 1)/(-2x - 3)) + 1| - 2) + 1, g(x) = (-2(1|x + 1| + 2) + 3)/(3(1|x + 1| + 2) + 2), x = -1.4, and x = -0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 2.0 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(5(2x^2 + 4x) - 1) + 1| + 1 and g(x) = (-2(-3x^2 - 4x - 1) + 2)/(-1(-3x^2 - 4x - 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}",
... | 0.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1|((-2(-1x^2 - 4) + 2)/(-1(-1x^2 - 4) - 3)) + 1| + 2, g(x) = 1cos(2π(3x - 4)) - 1, x = 4.2, and x = 4.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | MATH |
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