messages listlengths 1 1 | ground_truth stringlengths 3 7 | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Calculate the area enclosed between the functions f(x) = 3(-2|(4(-3sin(1π((-3(-4x^2 + 5x + 3) + 1)/(-2(-4x^2 + 5x + 3) - 3)) - 2) + 1)^2 - 5(-3sin(1π((-3(-4x^2 + 5x + 3) + 1)/(-2(-4x^2 + 5x + 3) - 3)) - 2) + 1) + 3) - 2| + 2) + 1 and g(x) = -1|(1(3cos(2π(-1|(2|x| - 1) + 2| - 2) - 3) - 3) - 4) - 3|... | 8.6 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(-1|(-3e^(-1(4(1|(3x^2 - 1x + 5) - 3| - 1)^2 - 2(1|(3x^2 - 1x + 5) - 3| - 1) - 4)) + 3) + 3| + 3) + 3)/(-3(-1|(-3e^(-1(4(1|(3x^2 - 1x + 5) - 3| - 1)^2 - 2(1|(3x^2 - 1x + 5) - 3| - 1) - 4)) + 3) + 3| + 3)) and g(x) = -2|(3(1|((2(-... | 1.0 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (2(1((2((-2(3(1|x + 2| - 1)^2 + 4(1|x + 2| - 1) + 1) + 1)/(3(3(1|x + 2| - 1)^2 + 4(1|x + 2| - 1) + 1) + 2)) - 2)/(2((-2(3(1|x + 2| - 1)^2 + 4(1|x + 2| - 1) + 1) + 1)/(3(3(1|x + 2| - 1)^2 + 4(1|x + 2| - 1) + 1) + 2)) - 1)) + 5) - 1)/(2(1((2((... | 0.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (1(2|(-2|(-1e^(1(-3|(1x^2 - 2x - 4) - 2|))) - 2| + 2) + 3| - 3) + 3)/(3(2|(-2|(-1e^(1(-3|(1x^2 - 2x - 4) - 2|))) - 2| + 2) + 3| - 3) - 2) and g(x) = -2(-5(-2sin(1π(-2|(-2|x + 1|) - 3| - 3) + 2) + 1) - 4)^2 - 3(-5(-2sin(1π(-2|(-2|x + 1|) - 3|... | 1.9 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -2|((3((-3(2|(3cos(1π((-3x - 1)/(-1x + 3)) - 1) - 2) + 2| + 2) - 1)/(3(2|(3cos(1π((-3x - 1)/(-1x + 3)) - 1) - 2) + 2| + 2) + 1)))/(1((-3(2|(3cos(1π((-3x - 1)/(-1x + 3)) - 1) - 2) + 2| + 2) - 1)/(3(2|(3cos(1π((-3x - 1)/(-1x + 3)) - 1) - 2) + ... | 2.5 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -5((-1(1|(-1|(-4(1x^2 - 1) - 1) - 2| + 1) + 3| - 3) - 2)/(1(1|(-1|(-4(1x^2 - 1) - 1) - 2| + 1) + 3| - 3))) - 4 and g(x) = -1|(5(3|(1((-1x - 1)/(-3x + 2))^2 - 5((-1x - 1)/(-3x + 2)) + 3) - 1| + 2) - 2)| - 3 between the vertical lines... | 68.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-2(-3(2|(1((-2((3x + 3)/(-1x)) - 1)/(2((3x + 3)/(-1x)) - 3))^2 + 5) - 3|) + 2) + 1)/(1(-3(2|(1((-2((3x + 3)/(-1x)) - 1)/(2((3x + 3)/(-1x)) - 3))^2 + 5) - 3|) + 2) - 3), g(x) = (-1((-1(1|(-3(-2|x - 3|)^2 - 5(-2|x - 3|) - 1) + 2|) - 1)/(3(1|(... | 1.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1cos(1π(3(2|(1((1((-1x - 3)/(1x)) + 2)/(-2((-1x - 3)/(1x)) + 3))^2 + 5) - 3|) - 5) - 2) + 2 and g(x) = 1(-1((2(2(5x - 4) - 3) - 1)/(-3(2(5x - 4) - 3) - 3)) - 1)^2 + 1(-1((2(2(5x - 4) - 3) - 1)/(-3(2(5x - 4) - 3) - 3)) - 1) - 3 betwe... | -0.8 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1((1(5((1(-3|((-3x - 3)/(-1x)) + 3| - 2) - 2)/(2(-3|((-3x - 3)/(-1x)) + 3| - 2) - 1))^2 + 3((1(-3|((-3x - 3)/(-1x)) + 3| - 2) - 2)/(2(-3|((-3x - 3)/(-1x)) + 3| - 2) - 1)) + 1) + 2)/(2(5((1(-3|((-3x - 3)/(-1x)) + 3| - 2) - 2)/(2(-3|((-3x - 3)... | 0.0 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3|((3(2(2e^(1((2(1|x + 1| + 3) - 2)/(3(1|x + 1| + 3) + 3))) + 2)^2 + 5(2e^(1((2(1|x + 1| + 3) - 2)/(3(1|x + 1| + 3) + 3))) + 2) - 3) - 2)/(-3(2(2e^(1((2(1|x + 1| + 3) - 2)/(3(1|x + 1| + 3) + 3))) + 2)^2 + 5(2e^(1((2(1|x + 1| + 3) - ... | 0.4 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(-3((-1(-4((3(4x + 5))/(-3(4x + 5) - 2))^2 - 2((3(4x + 5))/(-3(4x + 5) - 2)) + 5) - 1)/(-2(-4((3(4x + 5))/(-3(4x + 5) - 2))^2 - 2((3(4x + 5))/(-3(4x + 5) - 2)) + 5) + 1)) + 5) and g(x) = 3((-2((-2(-1|(3x^2 + 1) - 2| - 1) - 3)/(-3(-... | 5.7 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 5(5(2|(2(-3(-2x - 4) - 4) - 3)| - 3))^2 - 4, g(x) = -1|(3(2((-2(-1x - 4) + 3)/(-2(-1x - 4) - 2))^2 - 5((-2(-1x - 4) + 3)/(-2(-1x - 4) - 2))) + 4)| + 3, x = -1.0, and x = -0.9. Round your answer to 1 decimal place.\n\nPresent the answer in La... | 6.0 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1((-2(2|((-2(-2cos(2π(-1x^2 - 2)) - 2) - 3)/(-3(-2cos(2π(-1x^2 - 2)) - 2) - 1)) + 2| + 3) + 3)/(-1(2|((-2(-2cos(2π(-1x^2 - 2)) - 2) - 3)/(-3(-2cos(2π(-1x^2 - 2)) - 2) - 1)) + 2| + 3) + 2)) - 3 and g(x) = 2(-5(4(2|(2x^2 - 5x - 4) + ... | 6.8 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (2(-1((1(1((3((-2x - 1)/(2x - 1)))/(-1((-2x - 1)/(2x - 1)) - 3))^2 - 5((3((-2x - 1)/(2x - 1)))/(-1((-2x - 1)/(2x - 1)) - 3)) + 4) - 2)/(-1(1((3((-2x - 1)/(2x - 1)))/(-1((-2x - 1)/(2x - 1)) - 3))^2 - 5((3((-2x - 1)/(2x - 1)))/(-1((-2x - 1)/(2... | 0.5 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-3((-2(1(-1(1|(1x^2 - 3x + 1) - 2| + 3) + 4)^2 + 4(-1(1|(1x^2 - 3x + 1) - 2| + 3) + 4) - 1) - 1)/(-1(1(-1(1|(1x^2 - 3x + 1) - 2| + 3) + 4)^2 + 4(-1(1|(1x^2 - 3x + 1) - 2| + 3) + 4) - 1) + 2)))/(1((-2(1(-1(1|(1x^2 - 3x + 1) - 2| + 3) + 4)^2 ... | 11.4 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (1(-1|(-2(-3(2cos(3π(2|x - 3| + 3) - 3) + 2) + 3) + 3) - 2|))/(-1(-1|(-2(-3(2cos(3π(2|x - 3| + 3) - 3) + 2) + 3) + 3) - 2|) - 2) and g(x) = 3(-2|(-1|(2|(5x + 5) - 3| + 2) - 1|) + 2| - 1)^2 - 1(-2|(-1|(2|(5x + 5) - 3| + 2) - 1|) + 2| - 1) - 2... | 1.7 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1|(-4(-1|((1((1(1e^(1x) - 3) + 2)/(1(1e^(1x) - 3))) + 3)/(3((1(1e^(1x) - 3) + 2)/(1(1e^(1x) - 3))) - 2)) + 3| - 1)) - 2|, g(x) = (-3(5(2|((1(-2sin(1πx + 1) + 2) - 2)/(-2(-2sin(1πx + 1) + 2) - 3)) - 1| - 2)^2 - 2(2|((1(-2sin(1πx + 1) + 2) - 2... | 41.8 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -4((-2(-4(3(-2|(1|x - 1| - 2) + 1| + 3) + 2) + 5) + 2)/(1(-4(3(-2|(1|x - 1| - 2) + 1| + 3) + 2) + 5))) + 3 and g(x) = -2(1|(-1((1(2x^2 + 4x - 5))/(2(2x^2 + 4x - 5) + 3)) - 5) - 3| - 3)^2 + 4(1|(-1((1(2x^2 + 4x - 5))/(2(2x^2 + 4x - 5) + 3)) -... | 289.9 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3|(1(1(2|((-2(-5x^2 - 1x + 1) + 3)/(-2(-5x^2 - 1x + 1) + 3)) - 2| + 2)) + 2)|, g(x) = (2(-5((2(1(-3e^(-1x) + 1)^2 + 3(-3e^(-1x) + 1) - 3) - 2)/(3(1(-3e^(-1x) + 1)^2 + 3(-3e^(-1x) + 1) - 3) - 2))^2 - 1((2(1(-3e^(-1x) + 1)^2 + 3(-3e^(-1x) + 1)... | 85.5 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -2|(4(1|(-2cos(1π(1|((-3x + 3)/(2x)) - 3| - 3) - 3) - 3) + 3|)^2 + 5(1|(-2cos(1π(1|((-3x + 3)/(2x)) - 3| - 3) - 3) - 3) + 3|) - 5) - 2| - 3 and g(x) = -1(4((2((1(-5x - 3) - 1)/(-2(-5x - 3) + 3)) + 1)/(-1((1(-5x - 3) - 1)/(-2(-5x - 3) + 3)) +... | 1.5 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-1(1(-1(-4((3(2cos(3πx - 1)) + 2)/(-2(2cos(3πx - 1)) + 3)) + 3) - 4)^2 - 2(-1(-4((3(2cos(3πx - 1)) + 2)/(-2(2cos(3πx - 1)) + 3)) + 3) - 4) - 4) + 1)/(3(1(-1(-4((3(2cos(3πx - 1)) + 2)/(-2(2cos(3πx - 1)) + 3)) + 3) - 4)^2 - 2(-1(-4((3(2cos(3π... | 0.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (3(-3|(2|(1|(5((2x)/(2x - 3)) - 4) - 2| - 1) + 1| + 1) - 3| + 3) + 2)/(-3(-3|(2|(1|(5((2x)/(2x - 3)) - 4) - 2| - 1) + 1| + 1) - 3| + 3) + 2), g(x) = 2((1(1(2(-2x^2 + 1x - 2) - 1)) + 1)/(-2(1(2(-2x^2 + 1x - 2) - 1)) + 1)), x = -1.3, and x = 2... | 0.5 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (2(-1e^(-1(-1(-1|(2|(-2|x| - 2) + 2| + 2) + 2| + 3)^2 - 4(-1|(2|(-2|x| - 2) + 2| + 2) + 2| + 3) + 5)) - 1) + 2)/(-2(-1e^(-1(-1(-1|(2|(-2|x| - 2) + 2| + 2) + 2| + 3)^2 - 4(-1|(2|(-2|x| - 2) + 2| + 2) + 2| + 3) + 5)) - 1) - 3) and g(x) = (3((-... | 19.0 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-2(-5((-3(2((3(4x - 2) + 3)/(1(4x - 2) - 2))^2 - 5((3(4x - 2) + 3)/(1(4x - 2) - 2)) - 4) - 2)/(1(2((3(4x - 2) + 3)/(1(4x - 2) - 2))^2 - 5((3(4x - 2) + 3)/(1(4x - 2) - 2)) - 4) - 2)) + 3) - 1)/(1(-5((-3(2((3(4x - 2) + 3)/(1(4x - 2) - 2))^2 -... | 0.7 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(-3(3(-3((3(3sin(3πx + 3) - 1) - 3)/(1(3sin(3πx + 3) - 1) + 3))^2 - 4((3(3sin(3πx + 3) - 1) - 3)/(1(3sin(3πx + 3) - 1) + 3)) - 1) + 1) + 3) - 3)/(-2(-3(3(-3((3(3sin(3πx + 3) - 1) - 3)/(1(3sin(3πx + 3) - 1) + 3))^2 - 4((3(3sin(3πx ... | 0.4 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1((-1(-1(-3(-3(-1|x + 3|)^2 - 1(-1|x + 3|) + 3) + 5) - 2) - 2)/(2(-1(-3(-3(-1|x + 3|)^2 - 1(-1|x + 3|) + 3) + 5) - 2) + 3)) + 1, g(x) = (1(3(-3|((2((-2x)/(-3x + 4)) + 1)/(1((-2x)/(-3x + 4)) + 1))| - 2)^2 - 4(-3|((2((-2x)/(-3x + 4)) + 1)/(1(... | 3.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(1(1(1|((2(-3x + 5) - 2)/(-1(-3x + 5) - 1)) - 2| - 3)^2 - 3(1|((2(-3x + 5) - 2)/(-1(-3x + 5) - 1)) - 2| - 3) - 4) + 1)^2 - 1(1(1(1|((2(-3x + 5) - 2)/(-1(-3x + 5) - 1)) - 2| - 3)^2 - 3(1|((2(-3x + 5) - 2)/(-1(-3x + 5) - 1)) - 2| - 3... | 0.3 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|(-3cos(3π((2(2|(-1(-2|x - 1| + 3)^2 + 5(-2|x - 1| + 3) - 5)| + 3) - 1)/(1(2|(-1(-2|x - 1| + 3)^2 + 5(-2|x - 1| + 3) - 5)| + 3) - 3)) - 1) - 2) - 3| + 3 and g(x) = 1((-2(-4(-3(-2x^2 - 1x + 2) + 5) - 3) + 2)/(1(-4(-3(-2x^2 - 1x + 2)... | 0.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|(2(3(3(3(-2|x| - 1)^2 - 1(-2|x| - 1) - 5)) + 3) + 2) + 1| + 2 and g(x) = 1(2cos(1π(-2(5(3x^2 + 3x - 5) - 4) + 5) + 3) + 2) - 4 between the vertical lines x = -0.0 and x = 0.1. Round to 1 decimal place.\n\nPresent the answer in La... | 1.9 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (3(4(-4(2(2sin(2π((2x + 2)/(-1x)) + 3) - 1) + 3)^2 - 3(2(2sin(2π((2x + 2)/(-1x)) + 3) - 1) + 3) + 5)^2 - 4(-4(2(2sin(2π((2x + 2)/(-1x)) + 3) - 1) + 3)^2 - 3(2(2sin(2π((2x + 2)/(-1x)) + 3) - 1) + 3) + 5) - 1) + 3)/(-2(4(-4(2(2sin(2π((2x + 2)/... | 0.8 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3((-3((1((1((-2(5x^2 + 1x - 5) - 3)/(-2(5x^2 + 1x - 5) + 1)) - 2)/(-2((-2(5x^2 + 1x - 5) - 3)/(-2(5x^2 + 1x - 5) + 1)) + 3)) - 3)/(1((1((-2(5x^2 + 1x - 5) - 3)/(-2(5x^2 + 1x - 5) + 1)) - 2)/(-2((-2(5x^2 + 1x - 5) - 3)/(-2(5x^2 + 1x - 5) + 1)... | 4.4 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 4((3((-3(-2((3(2|x + 2| + 3) + 2)/(-3(2|x + 2| + 3) + 2))^2 + 2((3(2|x + 2| + 3) + 2)/(-3(2|x + 2| + 3) + 2)) - 3) - 2)/(1(-2((3(2|x + 2| + 3) + 2)/(-3(2|x + 2| + 3) + 2))^2 + 2((3(2|x + 2| + 3) + 2)/(-3(2|x + 2| + 3) + 2)) - 3))) - 1)/(3((-... | 1.6 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(-1(1cos(1π((2(1(-2x^2 - 1x - 4) + 5) + 3)/(-1(1(-2x^2 - 1x - 4) + 5) - 3))) - 1) + 4)^2 - 3(-1(1cos(1π((2(1(-2x^2 - 1x - 4) + 5) + 3)/(-1(1(-2x^2 - 1x - 4) + 5) - 3))) - 1) + 4) + 5 and g(x) = -3|(-2|(3|(-2cos(1π(3|x + 1| - 2) + ... | 8.7 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2(-2|(2(1(-2(2x + 1) + 1)^2 + 1(-2(2x + 1) + 1) - 1)^2 - 3(1(-2(2x + 1) + 1)^2 + 1(-2(2x + 1) + 1) - 1) + 4) - 1| + 2)^2 - 4(-2|(2(1(-2(2x + 1) + 1)^2 + 1(-2(2x + 1) + 1) - 1)^2 - 3(1(-2(2x + 1) + 1)^2 + 1(-2(2x + 1) + 1) - 1) + 4) - 1| + 2... | 0.5 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -4(-2|(2sin(1π((-3((3((-2x - 2)/(3x - 1)))/(3((-2x - 2)/(3x - 1)) - 2)) + 3)/(2((3((-2x - 2)/(3x - 1)))/(3((-2x - 2)/(3x - 1)) - 2)) - 1)) + 2) - 3)| + 2)^2 + 3(-2|(2sin(1π((-3((3((-2x - 2)/(3x - 1)))/(3((-2x - 2)/(3x - 1)) - 2)) + 3)/(2((3(... | 6.5 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1((-3(2(-3|((3((1x + 2)/(-3x - 3)) - 2)/(-2((1x + 2)/(-3x - 3)) + 3)) + 2| - 3)^2 - 2(-3|((3((1x + 2)/(-3x - 3)) - 2)/(-2((1x + 2)/(-3x - 3)) + 3)) + 2| - 3) - 4) + 1)/(2(2(-3|((3((1x + 2)/(-3x - 3)) - 2)/(-2((1x + 2)/(-3x - 3)) + 3... | 0.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 4(-5(2(1|(3(-1x + 4) - 2) + 1|)^2 + 1(1|(3(-1x + 4) - 2) + 1|) - 5) - 1) - 5 and g(x) = -3cos(2π(1|(1|(-1((3x - 1)/(-3x + 4)) + 3) - 1| + 1) + 2| - 3) - 1) - 2 from x = 3.2 to x = 4.1. Round to 1 decimal place.\n\nPresent the answer in LaTex... | 49.7 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 4(-1|(-1|((1(5(1sin(3πx - 2) + 2)^2 - 5(1sin(3πx - 2) + 2) + 1) + 2)/(1(5(1sin(3πx - 2) + 2)^2 - 5(1sin(3πx - 2) + 2) + 1) - 3)) + 2| - 3) + 2| + 3) - 1, g(x) = 2cos(1π(-2|(-1(-4(5x^2 + 5x) - 5)^2 + 5(-4(5x^2 + 5x) - 5) + 1)| + 1) - 1), x = ... | 8.0 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2((-2(3|(1|(-1(-1|x - 3| - 3) + 5)|) - 2| + 2) + 2)/(2(3|(1|(-1(-1|x - 3| - 3) + 5)|) - 2| + 2) + 1))^2 + 3((-2(3|(1|(-1(-1|x - 3| - 3) + 5)|) - 2| + 2) + 2)/(2(3|(1|(-1(-1|x - 3| - 3) + 5)|) - 2| + 2) + 1)), g(x) = -5(2cos(2π((2(-4((3x - 3... | 0.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (1(-1(-5(-1cos(1π(5(-4x - 3) + 2) + 2) - 3)^2 + 5(-1cos(1π(5(-4x - 3) + 2) + 2) - 3)) - 2) - 1)/(1(-1(-5(-1cos(1π(5(-4x - 3) + 2) + 2) - 3)^2 + 5(-1cos(1π(5(-4x - 3) + 2) + 2) - 3)) - 2) + 3), g(x) = (-2(1|(-2((3(1|x + 2| - 2) - 3)/(-2(1|x +... | 0.6 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-1((-2(1(4(-2(3|x + 2|)^2 - 4(3|x + 2|) + 2)^2 + 2(-2(3|x + 2|)^2 - 4(3|x + 2|) + 2) - 5) - 3) + 1)/(-1(1(4(-2(3|x + 2|)^2 - 4(3|x + 2|) + 2)^2 + 2(-2(3|x + 2|)^2 - 4(3|x + 2|) + 2) - 5) - 3))) - 2)/(-1((-2(1(4(-2(3|x + 2|)^2 - 4(3|x + 2|) ... | 3.2 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2(1(3e^(-1(2|(2(-2x^2 + 4x + 2)^2 - 1(-2x^2 + 4x + 2) - 5)| + 2)) - 2) + 4)^2 + 4(1(3e^(-1(2|(2(-2x^2 + 4x + 2)^2 - 1(-2x^2 + 4x + 2) - 5)| + 2)) - 2) + 4) - 3, g(x) = -2cos(2π(-5((2(2|((2x)/(3x + 3)) - 3| - 3) - 2)/(-3(2|((2x)/(3x + 3)) - ... | 0.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (3((-3(3|(-3|(-2((2x - 2)/(-1x - 2)) - 3)| + 2) - 3| - 3) - 3)/(3(3|(-3|(-2((2x - 2)/(-1x - 2)) - 3)| + 2) - 3| - 3))))/(-3((-3(3|(-3|(-2((2x - 2)/(-1x - 2)) - 3)| + 2) - 3| - 3) - 3)/(3(3|(-3|(-2((2x - 2)/(-1x - 2)) - 3)| + 2) - 3| - 3))) -... | 0.8 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 5(1((3(2sin(3π((2(-4x^2 - 2x + 1))/(-1(-4x^2 - 2x + 1) + 3)) + 1) - 1) + 3)/(3(2sin(3π((2(-4x^2 - 2x + 1))/(-1(-4x^2 - 2x + 1) + 3)) + 1) - 1) + 2))^2 + 2) + 4 and g(x) = -5(-3(-2(-1(-4x - 4)^2 + 2(-4x - 4) + 2) + 5)^2 - 5(-2(-1(-4x... | 1.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (1(4(1(-1(-2cos(1π(1x - 2) - 2) - 2) + 2) - 1)^2 - 5(1(-1(-2cos(1π(1x - 2) - 2) - 2) + 2) - 1) + 2) - 1)/(2(4(1(-1(-2cos(1π(1x - 2) - 2) - 2) + 2) - 1)^2 - 5(1(-1(-2cos(1π(1x - 2) - 2) - 2) + 2) - 1) + 2) - 3) and g(x) = -5(4(-5(1|((-1x + 3)... | 52.8 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1(2((-1(-1(-3|(3|x|)| - 1)^2 - 4(-3|(3|x|)| - 1) - 2) - 2)/(3(-1(-3|(3|x|)| - 1)^2 - 4(-3|(3|x|)| - 1) - 2) - 2)) + 5)^2 - 5(2((-1(-1(-3|(3|x|)| - 1)^2 - 4(-3|(3|x|)| - 1) - 2) - 2)/(3(-1(-3|(3|x|)| - 1)^2 - 4(-3|(3|x|)| - 1) - 2) - 2)) + 5)... | 0.3 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 4(1|(-3cos(2π((2(5(-3|x + 3|)^2 + 2(-3|x + 3|) + 2) - 1)/(1(5(-3|x + 3|)^2 + 2(-3|x + 3|) + 2) + 2)) - 3) + 2)| - 1) - 3 and g(x) = -2(-2|(-2sin(1π(-3|(1|x - 1|)| - 1) + 3) + 3) + 3| + 3) - 3 from x = -0.3 to x = -0.0. Round to 1 decimal pla... | 1.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(3((2(-3(-1((3x)/(2x + 3))^2 + 5((3x)/(2x + 3)) + 4)) - 3)/(3(-3(-1((3x)/(2x + 3))^2 + 5((3x)/(2x + 3)) + 4)) - 1))^2 - 2((2(-3(-1((3x)/(2x + 3))^2 + 5((3x)/(2x + 3)) + 4)) - 3)/(3(-3(-1((3x)/(2x + 3))^2 + 5((3x)/(2x + 3)) + 4)) - ... | 0.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-2((-1(-2(-3cos(1π((-1(4x + 5))/(2(4x + 5))) - 1) + 2) + 2))/(-2(-2(-3cos(1π((-1(4x + 5))/(2(4x + 5))) - 1) + 2) + 2) + 1)) + 1)/(2((-1(-2(-3cos(1π((-1(4x + 5))/(2(4x + 5))) - 1) + 2) + 2))/(-2(-2(-3cos(1π((-1(4x + 5))/(2(4x + 5))) - 1) + 2... | 133.4 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1((-1(2|(1|((2(3x^2 + 4x - 3))/(-1(3x^2 + 4x - 3) + 2)) - 3| + 1)| + 2) + 3)/(3(2|(1|((2(3x^2 + 4x - 3))/(-1(3x^2 + 4x - 3) + 2)) - 3| + 1)| + 2) + 2))^2 - 2((-1(2|(1|((2(3x^2 + 4x - 3))/(-1(3x^2 + 4x - 3) + 2)) - 3| + 1)| + 2) + 3)/(3(2|(1|... | 26.6 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 2|(2|(-3|((-3(1(1x - 2)^2 + 3) + 2)/(1(1(1x - 2)^2 + 3) + 2)) - 3| - 2) + 3| + 1) - 3| + 3, g(x) = (2(1|(-2|((3((-2x + 1)/(1x + 1)) - 3)/(1((-2x + 1)/(1x + 1)) + 1)) - 3|) + 3| - 3) + 1)/(-2(1|(-2|((3((-2x + 1)/(1x + 1)) - 3)/(1((-2x + 1)/(1... | 41.6 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(-1((-1((-3(2|(3|x - 1| - 1) + 2| - 3))/(-1(2|(3|x - 1| - 1) + 2| - 3) + 2)) + 3)/(2((-3(2|(3|x - 1| - 1) + 2| - 3))/(-1(2|(3|x - 1| - 1) + 2| - 3) + 2))))^2 + 4((-1((-3(2|(3|x - 1| - 1) + 2| - 3))/(-1(2|(3|x - 1| - 1) + 2| - 3) ... | 0.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3((-2((2(-5(-5(-5x^2 - 3x + 5)^2 + 4(-5x^2 - 3x + 5) + 2) - 5) - 2)/(2(-5(-5(-5x^2 - 3x + 5)^2 + 4(-5x^2 - 3x + 5) + 2) - 5) + 3)) + 3)/(2((2(-5(-5(-5x^2 - 3x + 5)^2 + 4(-5x^2 - 3x + 5) + 2) - 5) - 2)/(2(-5(-5(-5x^2 - 3x + 5)^2 + ... | 6.0 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -5((2(-3|(1(-3|(2|x - 2| + 2) - 3| - 1)^2 + 1(-3|(2|x - 2| + 2) - 3| - 1) - 1) - 2| + 1) - 1)/(1(-3|(1(-3|(2|x - 2| + 2) - 3| - 1)^2 + 1(-3|(2|x - 2| + 2) - 3| - 1) - 1) - 2| + 1) + 3)) - 2 and g(x) = (-2(-2|((-3(-1cos(1π(1x - 2) + ... | 26.5 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (1(3(-5((-3(1(2|x| + 3)^2 + 4(2|x| + 3) + 4) - 1)/(2(1(2|x| + 3)^2 + 4(2|x| + 3) + 4) + 2)) + 2)) - 2)/(-3(3(-5((-3(1(2|x| + 3)^2 + 4(2|x| + 3) + 4) - 1)/(2(1(2|x| + 3)^2 + 4(2|x| + 3) + 4) + 2)) + 2)) - 3) and g(x) = -2e^(1((-2((2(-1|(5x^2 ... | 0.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (3(-2(5(1|(-1|(-1|x - 1| - 1) + 1| - 3) - 1| + 2)^2 - 3(1|(-1|(-1|x - 1| - 1) + 1| - 3) - 1| + 2) - 5)^2 + 3(5(1|(-1|(-1|x - 1| - 1) + 1| - 3) - 1| + 2)^2 - 3(1|(-1|(-1|x - 1| - 1) + 1| - 3) - 1| + 2) - 5) + 3) - 3)/(1(-2(5(1|(-1|(-1|x - 1| ... | 0.0 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -5(-3|((-2(1(3sin(2π(-2|x| + 2) + 3) + 2)^2 - 2(3sin(2π(-2|x| + 2) + 3) + 2) + 1) + 3)/(-3(1(3sin(2π(-2|x| + 2) + 3) + 2)^2 - 2(3sin(2π(-2|x| + 2) + 3) + 2) + 1) - 1)) + 3| - 1)^2 + 3(-3|((-2(1(3sin(2π(-2|x| + 2) + 3) + 2)^2 - 2(3sin(2π(-2|x... | 270.9 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2|((2(3|(-1|(2(1x^2 - 2x + 2)^2 + 3(1x^2 - 2x + 2) - 5) + 2| + 1) + 2| - 1) - 3)/(1(3|(-1|(2(1x^2 - 2x + 2)^2 + 3(1x^2 - 2x + 2) - 5) + 2| + 1) + 2| - 1)))|, g(x) = -1|(4(4(-2|(4x - 5) + 2| - 1)^2 + 5(-2|(4x - 5) + 2| - 1) + 4)^2 + 4(4(-2|(... | 6.8 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(-2((1(-3|(5(-4x^2 - 3x - 4)^2 + 3(-4x^2 - 3x - 4) - 3) - 3| + 2))/(-3(-3|(5(-4x^2 - 3x - 4)^2 + 3(-4x^2 - 3x - 4) - 3) - 3| + 2) - 2))^2 - 4((1(-3|(5(-4x^2 - 3x - 4)^2 + 3(-4x^2 - 3x - 4) - 3) - 3| + 2))/(-3(-3|(5(-4x^2 - 3x - 4)... | 1.0 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1|((3(-3sin(1π(1|(-1(-1|x + 3| + 2) + 5) + 1| - 3)) - 1) + 1)/(-2(-3sin(1π(1|(-1(-1|x + 3| + 2) + 5) + 1| - 3)) - 1) + 3)) - 3| + 3 and g(x) = -3cos(2π(5((3(-1(5x - 3) + 5) + 2)/(-1(-1(5x - 3) + 5) + 3)) + 2) - 3) + 1 from x = 3.2 to x = 3.3... | 0.6 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-2(2(5((1(-2((3x + 2)/(2x + 2))^2 + 4((3x + 2)/(2x + 2)) + 1) - 1)/(-2(-2((3x + 2)/(2x + 2))^2 + 4((3x + 2)/(2x + 2)) + 1)))^2 - 5((1(-2((3x + 2)/(2x + 2))^2 + 4((3x + 2)/(2x + 2)) + 1) - 1)/(-2(-2((3x + 2)/(2x + 2))^2 + 4((3x + 2)/(2x + 2)... | 0.7 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 2|(1(-2((2(-4(-3|x + 3| + 3) + 5))/(-2(-4(-3|x + 3| + 3) + 5) + 1))^2 + 1((2(-4(-3|x + 3| + 3) + 5))/(-2(-4(-3|x + 3| + 3) + 5) + 1)) - 3) - 1) + 1| + 1, g(x) = 2|(-1((3(2|(-4x - 4) - 1| + 3) - 1)/(3(2|(-4x - 4) - 1| + 3) - 2)) - 2)| + 2, x ... | 3.9 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1(2e^(2(-2(2|(1(1|x|)^2) + 1| - 1)^2 + 5)) - 3) - 4, g(x) = -1((-2(2cos(3π(-2(3x - 1))) + 2) - 3)/(2(2cos(3π(-2(3x - 1))) + 2) + 3)) + 5, x = -0.5, and x = 0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\b... | 331.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2(1|(5(-2|((-2(4x^2 - 4x - 5) - 1)/(3(4x^2 - 4x - 5))) + 1| + 3)^2 + 3(-2|((-2(4x^2 - 4x - 5) - 1)/(3(4x^2 - 4x - 5))) + 1| + 3) + 3) - 3|)^2 + 4(1|(5(-2|((-2(4x^2 - 4x - 5) - 1)/(3(4x^2 - 4x - 5))) + 1| + 3)^2 + 3(-2|((-2(4x^2 - 4x - 5) - 1... | 43.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-1(-3|(-3(-3|(1|(-2|x - 2| + 3) + 2| - 2) + 1| + 3)^2 + 3(-3|(1|(-2|x - 2| + 3) + 2| - 2) + 1| + 3))|) - 1)/(-3(-3|(-3(-3|(1|(-2|x - 2| + 3) + 2| - 2) + 1| + 3)^2 + 3(-3|(1|(-2|x - 2| + 3) + 2| - 2) + 1| + 3))|) - 1) and g(x) = 3e^(-2(5(1(2... | 0.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (2(-3|((-1(-1sin(2π(-4(5x^2 - 5x - 1) - 1) - 1) + 2) - 1)/(-3(-1sin(2π(-4(5x^2 - 5x - 1) - 1) - 1) + 2) - 2)) + 3| - 3) + 2)/(-1(-3|((-1(-1sin(2π(-4(5x^2 - 5x - 1) - 1) - 1) + 2) - 1)/(-3(-1sin(2π(-4(5x^2 - 5x - 1) - 1) - 1) + 2) - 2)) + 3| ... | 16.7 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 3(5(-1(-2|(-1(-5x^2 + 3x - 2)^2 - 5(-5x^2 + 3x - 2) + 5) + 1| - 2) - 5)^2 - 2(-1(-2|(-1(-5x^2 + 3x - 2)^2 - 5(-5x^2 + 3x - 2) + 5) + 1| - 2) - 5) - 2) - 4 and g(x) = (-1((2((1(2e^(-1(2|x - 1| - 1))) - 1)/(-1(2e^(-1(2|x - 1| - 1))) - 3)) + 3)... | 6.5 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -2|(4(-2e^(1(-2|(5(5x^2 - 1x + 5)^2 + 4(5x^2 - 1x + 5) + 3) - 3|)) - 2)^2 + 5(-2e^(1(-2|(5(5x^2 - 1x + 5)^2 + 4(5x^2 - 1x + 5) + 3) - 3|)) - 2) + 1)| - 2 and g(x) = -3|(-3(4(-3((-1x)/(-2x + 3)) - 2) + 2)^2 + 5(4(-3((-1x)/(-2x + 3)) - 2) + 2)... | 1.8 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -3|(2sin(1π(-5(2|(2|(5x^2 + 1x - 4) - 1| - 2) - 3| + 3)^2 + 4(2|(2|(5x^2 + 1x - 4) - 1| - 2) - 3| + 3) - 4) - 3) + 3) - 3| + 3, g(x) = -3(3sin(3π(3((3(2|x - 1| - 3) - 3)/(3(2|x - 1| - 3) - 2))) - 3) - 2)^2 + 2(3sin(3π(3((3(2|x - 1| - 3) - 3)... | 0.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1|((-1(-1|(-3(5((1x - 1)/(1x - 2)) + 1)^2 + 5(5((1x - 1)/(1x - 2)) + 1) + 5) - 1| + 3) - 1)/(-3(-1|(-3(5((1x - 1)/(1x - 2)) + 1)^2 + 5(5((1x - 1)/(1x - 2)) + 1) + 5) - 1| + 3) - 1)) + 1| + 3 and g(x) = 1(-3((1(3sin(1π(1x^2 + 2x + 2) - 3) + 1... | 62.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2|(-3e^(2(-3(-1(-1|(1|x - 2| + 3) - 1| + 1)^2 - 2(-1|(1|x - 2| + 3) - 1| + 1) + 1) - 1))) - 2| - 2, g(x) = 1(5((3(3(-2|x - 3| + 2)^2 + 4(-2|x - 3| + 2) - 4) + 2)/(2(3(-2|x - 3| + 2)^2 + 4(-2|x - 3| + 2) - 4) - 1)) + 5) + 1, x = 1.0, and x =... | 21.8 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1|((-3(-3|(-3(-1((-3x - 3)/(-1x + 2))^2 - 2((-3x - 3)/(-1x + 2)) - 1)^2 + 3(-1((-3x - 3)/(-1x + 2))^2 - 2((-3x - 3)/(-1x + 2)) - 1) - 4) + 2| + 1) + 3)/(-1(-3|(-3(-1((-3x - 3)/(-1x + 2))^2 - 2((-3x - 3)/(-1x + 2)) - 1)^2 + 3(-1((-3x - 3)/(-1... | 0.7 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -2|(1|(2((3((3(-4x^2 - 5x - 3) + 3)/(-1(-4x^2 - 5x - 3) + 2)) + 3)/(3((3(-4x^2 - 5x - 3) + 3)/(-1(-4x^2 - 5x - 3) + 2)) - 2)) - 4) + 2| - 1) + 3| - 1 and g(x) = -3|(4(-3(-1(2x^2 - 1x + 2)^2 + 2(2x^2 - 1x + 2) + 5) - 4) + 2) + 1| + 3 from x =... | 294.3 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(-3cos(3π((2(-3((-1(-2x^2 + 2x - 4))/(-3(-2x^2 + 2x - 4) + 1))^2 + 2((-1(-2x^2 + 2x - 4))/(-3(-2x^2 + 2x - 4) + 1)) - 3) - 2)/(-1(-3((-1(-2x^2 + 2x - 4))/(-3(-2x^2 + 2x - 4) + 1))^2 + 2((-1(-2x^2 + 2x - 4))/(-3(-2x^2 + 2x - 4) + 1... | 0.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|(3sin(1π(-5(1|((2((-2x - 2)/(-3x - 2)) + 3)/(-1((-2x - 2)/(-3x - 2)) + 3)) + 3| + 2) - 1) - 3) - 3) + 3| - 1 and g(x) = (-3((1(3|(-3|(-2|x - 1|) + 2| - 1) + 2| + 3) + 3)/(2(3|(-3|(-2|x - 1|) + 2| - 1) + 2| + 3) + 2)) + 1)/(1((1(3... | 19.8 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -4((-3(-4((2((2((1x - 1)/(1x + 1)) - 3)/(2((1x - 1)/(1x + 1)) - 3)) - 2)/(-3((2((1x - 1)/(1x + 1)) - 3)/(2((1x - 1)/(1x + 1)) - 3)) - 2)) - 5) + 1)/(-1(-4((2((2((1x - 1)/(1x + 1)) - 3)/(2((1x - 1)/(1x + 1)) - 3)) - 2)/(-3((2((1x - 1)/(1x + 1... | 19.9 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(-2|(1sin(3π(-1|((-3(2|x - 3| - 3) - 1)/(-2(2|x - 3| - 3) - 1)) - 3| + 3) + 3) + 1) + 3| + 2)^2 - 3(-2|(1sin(3π(-1|((-3(2|x - 3| - 3) - 1)/(-2(2|x - 3| - 3) - 1)) - 3| + 3) + 3) + 1) + 3| + 2) - 2 and g(x) = -1((-2(5((-1(-5x + 2) ... | 1.7 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -4(-3(2(-1((-2(1x + 3) - 1)/(-1(1x + 3) - 3))^2 + 4((-2(1x + 3) - 1)/(-1(1x + 3) - 3)) + 5) + 3)^2 + 1(2(-1((-2(1x + 3) - 1)/(-1(1x + 3) - 3))^2 + 4((-2(1x + 3) - 1)/(-1(1x + 3) - 3)) + 5) + 3) + 1) - 3, g(x) = -1((-3(-5(2(2|x|)^2 - 5(2|x|) ... | 0.6 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|((-3(-3|((-2(1(4x + 2) + 1))/(2(1(4x + 2) + 1) - 1)) + 1|) + 1)/(-2(-3|((-2(1(4x + 2) + 1))/(2(1(4x + 2) + 1) - 1)) + 1|) + 1)) + 3| + 2 and g(x) = 3((-1((3(-3(2x^2 - 1x - 5)^2 + 3) + 3)/(1(-3(2x^2 - 1x - 5)^2 + 3) - 2)) + 2)/(1(... | 3.0 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -3sin(2π(1(2|((-3(-5(5x + 5)^2 + 3(5x + 5) + 2))/(3(-5(5x + 5)^2 + 3(5x + 5) + 2))) + 2|)^2 + 3(2|((-3(-5(5x + 5)^2 + 3(5x + 5) + 2))/(3(-5(5x + 5)^2 + 3(5x + 5) + 2))) + 2|) - 3) - 3) + 1, g(x) = (3(3(-5(-2(-5x - 2)^2 - 4(-5x - 2) + 4)^2 - ... | 0.0 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2|(-1(-4((2(-2sin(2π((-1x - 1)/(1x + 2)) - 2) + 1) + 2)/(-3(-2sin(2π((-1x - 1)/(1x + 2)) - 2) + 1) + 2)) - 4) + 3)| + 2, g(x) = 4(-3|((2((-2(1x + 5) + 1)/(-1(1x + 5) - 1)) + 1)/(1((-2(1x + 5) + 1)/(-1(1x + 5) - 1)) - 3)) + 1|) + 2, x = -2.1... | 1.3 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-3(-3|(2(2(2sin(1π(-4x) - 3) - 2) + 5) - 4)| + 3) - 1)/(-1(-3|(2(2(2sin(1π(-4x) - 3) - 2) + 5) - 4)| + 3) + 2), g(x) = (-2(-2|((3(2(4x + 1) - 5))/(2(2(4x + 1) - 5) - 3)) + 2|) + 2)/(-2(-2|((3(2(4x + 1) - 5))/(2(2(4x + 1) - 5) - 3)) + 2|) + ... | 0.3 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1|((-3((2(2|(2|(3|x + 3| - 1) - 3| + 1) - 3| + 2) + 3)/(-3(2|(2|(3|x + 3| - 1) - 3| + 1) - 3| + 2) + 4)) + 1)/(1((2(2|(2|(3|x + 3| - 1) - 3| + 1) - 3| + 2) + 3)/(-3(2|(2|(3|x + 3| - 1) - 3| + 1) - 3| + 2) + 4)) + 3))| and g(x) = 4(1|(-3|((-1... | 2.8 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1sin(3π((2(-1(-3|(3(4x^2 - 5) - 2) - 2| - 1) - 5) + 3)/(3(-1(-3|(3(4x^2 - 5) - 2) - 2| - 1) - 5) + 3)) + 2) - 3, g(x) = -3cos(3π(3|(1|(-2(-3|x - 1| - 3)^2 - 2(-3|x - 1| - 3)) + 1| + 3) - 2|)) - 1, x = -3.2, and x = -3.1. Round your answer t... | 0.3 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3((2(2(1(1((-3x + 2)/(-1x))^2 + 5((-3x + 2)/(-1x)) + 2) - 1)^2 - 3(1(1((-3x + 2)/(-1x))^2 + 5((-3x + 2)/(-1x)) + 2) - 1) - 3) + 3)/(1(2(1(1((-3x + 2)/(-1x))^2 + 5((-3x + 2)/(-1x)) + 2) - 1)^2 - 3(1(1((-3x + 2)/(-1x))^2 + 5((-3x + 2)... | 1.0 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(3sin(1π(-3|(-3(2|(4x + 1)| + 1)^2 + 2(2|(4x + 1)| + 1) - 1) - 2| + 2))) - 3)/(3(3sin(1π(-3|(-3(2|(4x + 1)| + 1)^2 + 2(2|(4x + 1)| + 1) - 1) - 2| + 2))) - 2) and g(x) = -1((2(5((1(-4x^2 - 3) - 1)/(-1(-4x^2 - 3))) + 3) + 3)/(-3(5((... | 0.5 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -4((-1((3((-1(-1|(-2|x + 2| + 1) - 2| - 2))/(-2(-1|(-2|x + 2| + 1) - 2| - 2))) - 2)/(2((-1(-1|(-2|x + 2| + 1) - 2| - 2))/(-2(-1|(-2|x + 2| + 1) - 2| - 2))))) - 2)/(-2((3((-1(-1|(-2|x + 2| + 1) - 2| - 2))/(-2(-1|(-2|x + 2| + 1) - 2| - 2))) - ... | 0.2 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1((3((1(-3e^(-2((1(1x - 2) + 2)/(-2(1x - 2) - 3))) + 3) - 3)/(1(-3e^(-2((1(1x - 2) + 2)/(-2(1x - 2) - 3))) + 3))))/(-3((1(-3e^(-2((1(1x - 2) + 2)/(-2(1x - 2) - 3))) + 3) - 3)/(1(-3e^(-2((1(1x - 2) + 2)/(-2(1x - 2) - 3))) + 3))) - 2)) - 1, g... | 25.3 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1(1((2((-3(-1(3x^2 - 5x - 1)^2 + 2(3x^2 - 5x - 1) - 2) - 1)/(2(-1(3x^2 - 5x - 1)^2 + 2(3x^2 - 5x - 1) - 2) + 1)) - 1)/(-2((-3(-1(3x^2 - 5x - 1)^2 + 2(3x^2 - 5x - 1) - 2) - 1)/(2(-1(3x^2 - 5x - 1)^2 + 2(3x^2 - 5x - 1) - 2) + 1)) - 2)) + 3) +... | 5.5 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3(3sin(3π(2|(2(-3((-2x + 1)/(2x - 3)) - 2)^2 - 4(-3((-2x + 1)/(2x - 3)) - 2) - 5) + 2| + 2)) - 2) + 1 and g(x) = 1|(-2|((1(-1|(-1x + 5) - 1| - 1) - 1)/(1(-1|(-1x + 5) - 1| - 1) + 2)) + 2| - 1) - 2| - 2 between the vertical lines x =... | 1.0 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(-1|((-2(1(2(-3x + 3) - 5) - 3))/(-3(1(2(-3x + 3) - 5) - 3) - 3)) - 2| - 2) - 2| - 3 and g(x) = -1((-1(3(-4(4x - 3)^2 + 5) - 2) + 2)/(-3(3(-4(4x - 3)^2 + 5) - 2) - 2)) - 1 between the vertical lines x = 0.5 and x = 1.0. Round to ... | 6.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3(3|(-2|((1(3((2x + 2)/(1x))) - 3)/(1(3((2x + 2)/(1x))) + 3)) + 2| + 2) + 1| + 2) + 1 and g(x) = -2|(-1|(2(-3((1x)/(2x - 1))^2 - 5((1x)/(2x - 1))) + 5) - 2|) - 1| + 1 from x = 0.4 to x = 1.1. Round to 1 decimal place.\n\nPresent the answer ... | -10.2 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3sin(2π(-1|(4(-2(-1(2|x - 2| - 3)^2 + 3(2|x - 2| - 3) - 1) + 5) - 5) - 3| + 2) + 2) - 2, g(x) = -2|(-3|((-1((3((-2x - 3)/(-2x + 3)) + 1)/(-2((-2x - 3)/(-2x + 3)) + 3)) - 3)/(-2((3((-2x - 3)/(-2x + 3)) + 1)/(-2((-2x - 3)/(-2x + 3)) + 3)))) + ... | 0.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-2((-3((-3(-2cos(2π(-4((-2x + 1)/(-2x - 3))^2 - 3((-2x + 1)/(-2x - 3)) - 4) + 1) + 2) + 3)/(-2(-2cos(2π(-4((-2x + 1)/(-2x - 3))^2 - 3((-2x + 1)/(-2x - 3)) - 4) + 1) + 2) + 3)) - 2)/(2((-3(-2cos(2π(-4((-2x + 1)/(-2x - 3))^2 - 3((-2x + 1)/(-2... | 35.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 4(1(1|(1|(1cos(1π(5x - 5) - 2) + 1) - 1| - 3) - 1| + 2)^2 - 5(1|(1|(1cos(1π(5x - 5) - 2) + 1) - 1| - 3) - 1| + 2)) - 2 and g(x) = 2|(-2e^(1((1(5(2|x - 1| + 3)^2 + 1(2|x - 1| + 3) + 3) + 3)/(-2(5(2|x - 1| + 3)^2 + 1(2|x - 1| + 3) + 3) + 3))) ... | 0.7 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(5(-3((1(3cos(2π(-4x - 3) + 3) + 3) + 3)/(3(3cos(2π(-4x - 3) + 3) + 3) - 2))^2 + 1)^2 - 3) + 2 and g(x) = 1cos(1π(1|((2(-1((2x + 3)/(-2x + 3))^2 - 1))/(-1(-1((2x + 3)/(-2x + 3))^2 - 1) + 3)) - 1| - 1) + 3) - 2 between the vertical... | 0.9 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-2(3cos(3π(5(-4(4(-1x^2 + 4x - 5) + 1) + 2)^2 - 2(-4(4(-1x^2 + 4x - 5) + 1) + 2) + 4) + 1) + 3) - 1)/(3(3cos(3π(5(-4(4(-1x^2 + 4x - 5) + 1) + 2)^2 - 2(-4(4(-1x^2 + 4x - 5) + 1) + 2) + 4) + 1) + 3)), g(x) = (1((-1(3|(5(3x - 1)^2 - 1(3x - 1) ... | 1.5 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -2|((2(2(1((1(-2x - 1) - 1)/(-2(-2x - 1) - 1))) - 1) + 3)/(-2(2(1((1(-2x - 1) - 1)/(-2(-2x - 1) - 1))) - 1) + 3))| - 1 and g(x) = (2(2cos(2π(-1|(-1|(-2|x - 2| + 2) + 1| + 3) + 3| - 1) + 1) + 1) - 2)/(3(2cos(2π(-1|(-1|(-2|x - 2| + 2) + 1| + 3... | 0.8 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|((-3(4((2(2(2x + 4)^2 - 5(2x + 4) + 5) - 2)/(-1(2(2x + 4)^2 - 5(2x + 4) + 5) + 2))^2 + 1((2(2(2x + 4)^2 - 5(2x + 4) + 5) - 2)/(-1(2(2x + 4)^2 - 5(2x + 4) + 5) + 2)) - 5) - 3)/(2(4((2(2(2x + 4)^2 - 5(2x + 4) + 5) - 2)/(-1(2(2x + 4... | 0.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(3((-3((1(5(-1x^2 + 4x)^2 - 4(-1x^2 + 4x) - 4) - 3)/(1(5(-1x^2 + 4x)^2 - 4(-1x^2 + 4x) - 4) + 3)) + 1)/(-2((1(5(-1x^2 + 4x)^2 - 4(-1x^2 + 4x) - 4) - 3)/(1(5(-1x^2 + 4x)^2 - 4(-1x^2 + 4x) - 4) + 3)) + 3))^2 - 4((-3((1(5(-1x^2 + 4x... | 16.5 | MATH |
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