id
stringlengths 31
70
| setting_key
stringclasses 31
values | difficulty
stringclasses 1
value | level
int64 1
1
| messages
listlengths 1
1
| ground_truth
stringlengths 1
19
| dataset
stringclasses 1
value | omega_split
stringclasses 1
value | __index_level_0__
int64 0
160k
|
|---|---|---|---|---|---|---|---|---|
math_algebra_func_area_level_1_1_900
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2cos(1π(-1x - 2) - 3) + 1 and g(x) = -1x - 2 between the vertical lines x = -5.0 and x = -4.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
math
|
train
| 900 |
math_algebra_func_area_level_1_1_901
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1((1x)/(2x - 1))^2 + 2((1x)/(2x - 1)) + 4 and g(x) = 1x^2 - 3x - 3 between the vertical lines x = -1.6 and x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
9.2
|
math
|
train
| 901 |
math_algebra_func_area_level_1_1_902
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -2(2cos(2πx + 3) + 1) - 2 and g(x) = -3x + 4 from x = 3.4 to x = 3.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.2
|
math
|
train
| 902 |
math_algebra_func_area_level_1_1_903
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1cos(1π((-2x - 1)/(1x)) + 1) - 1 and g(x) = 3x^2 + 3x - 2 between the vertical lines x = 0.2 and x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
train
| 903 |
math_algebra_func_area_level_1_1_904
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -3(2cos(2πx - 2))^2 - 5(2cos(2πx - 2)) + 3, g(x) = (2x - 2)/(2x + 1), x = 3.5, and x = 4.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.5
|
math
|
train
| 904 |
math_algebra_func_area_level_1_1_905
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1sin(3π(1x^2 - 3x - 1)) - 2, g(x) = -3x + 5, x = 2.1, and x = 2.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
math
|
train
| 905 |
math_algebra_func_area_level_1_1_906
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(4x)^2 - 2(4x) - 3 and g(x) = 1|x - 2| - 3 between the vertical lines x = -0.2 and x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.5
|
math
|
train
| 906 |
math_algebra_func_area_level_1_1_907
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3|((1x - 2)/(-2x + 3))| - 1 and g(x) = (3x - 1)/(-3x + 2) from x = 0.8 to x = 1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
35.8
|
math
|
train
| 907 |
math_algebra_func_area_level_1_1_908
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (2(2cos(2πx + 1) - 1) + 3)/(-3(2cos(2πx + 1) - 1)), g(x) = -1x + 4, 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"
}
] |
2.0
|
math
|
train
| 908 |
math_algebra_func_area_level_1_1_909
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1(3cos(1πx) - 1) + 3, g(x) = -5x^2 - 4x + 2, x = -0.4, and x = 0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.4
|
math
|
train
| 909 |
math_algebra_func_area_level_1_1_910
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1(-3x)^2 + 3(-3x) and g(x) = -1|x| + 1 from x = -1.0 to x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.1
|
math
|
train
| 910 |
math_algebra_func_area_level_1_1_911
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 5((-2x + 1)/(1x - 3))^2 - 5((-2x + 1)/(1x - 3)) - 5 and g(x) = -2|x - 1| + 3 between the vertical lines x = -0.6 and x = 1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
12.3
|
math
|
train
| 911 |
math_algebra_func_area_level_1_1_912
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1((2x - 1)/(-2x - 3))^2 - 1((2x - 1)/(-2x - 3)) - 2 and g(x) = 4x^2 + 4x - 5 between the vertical lines x = -2.5 and x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-4.2
|
math
|
train
| 912 |
math_algebra_func_area_level_1_1_913
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3cos(2π(-1|x - 2|)) + 3 and g(x) = -4x - 1 from x = -1.6 to x = -1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.2
|
math
|
train
| 913 |
math_algebra_func_area_level_1_1_914
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2|(-2x^2 + 2x - 5) + 3| + 1 and g(x) = 5x^2 + 1 from x = -4.8 to x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
30.2
|
math
|
train
| 914 |
math_algebra_func_area_level_1_1_915
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (3((-1x - 2)/(-1x)))/(-3((-1x - 2)/(-1x)) - 1) and g(x) = -2x - 2 from x = -1.7 to x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8.3
|
math
|
train
| 915 |
math_algebra_func_area_level_1_1_916
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (2(-2|x + 3|) + 2)/(-2(-2|x + 3|) - 3), g(x) = 2x - 4, x = -3.8, and x = -2.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
19.2
|
math
|
train
| 916 |
math_algebra_func_area_level_1_1_917
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 5(-2x^2 + 3x)^2 + 4(-2x^2 + 3x) - 5 and g(x) = -1|x - 1| from x = -0.4 to x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.8
|
math
|
train
| 917 |
math_algebra_func_area_level_1_1_918
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(-2e^(1x) + 3)^2 + 5(-2e^(1x) + 3) + 5 and g(x) = 1|x + 2| - 2 between the vertical lines x = -0.4 and x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.8
|
math
|
train
| 918 |
math_algebra_func_area_level_1_1_919
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -4(-2cos(1πx + 3) - 3)^2 + 1(-2cos(1πx + 3) - 3) - 3 and g(x) = 2x - 2 between the vertical lines x = -4.1 and x = -3.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.4
|
math
|
train
| 919 |
math_algebra_func_area_level_1_1_920
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2e^(1(2x^2 - 4x + 3)) + 2, g(x) = -2x - 2, x = 0.8, and x = 1.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.2
|
math
|
train
| 920 |
math_algebra_func_area_level_1_1_921
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 2(-1sin(3πx + 1))^2 - 5(-1sin(3πx + 1)) + 1, g(x) = -3|x - 1| - 1, x = 1.0, and x = 1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
train
| 921 |
math_algebra_func_area_level_1_1_922
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(1cos(3πx - 2) - 1) + 3 and g(x) = 5x^2 - 2x - 5 between the vertical lines x = -1.1 and x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
19.3
|
math
|
train
| 922 |
math_algebra_func_area_level_1_1_923
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3e^(-2(-1x^2 - 2x + 2)) - 3, g(x) = (-3x + 1)/(-2x), x = 0.1, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.4
|
math
|
train
| 923 |
math_algebra_func_area_level_1_1_924
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1cos(2π(1|x - 1| + 2) + 1) - 2 and g(x) = (2x - 1)/(-3x - 3) between the vertical lines x = -2.7 and x = -2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.7
|
math
|
train
| 924 |
math_algebra_func_area_level_1_1_925
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3cos(1π(2|x - 1|) - 2) + 3, g(x) = 2|x + 2| - 3, x = 2.2, 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
|
train
| 925 |
math_algebra_func_area_level_1_1_926
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -3sin(3π(4x^2 - 4x + 2) + 3) + 3, g(x) = (-1x + 2)/(-1x - 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
|
train
| 926 |
math_algebra_func_area_level_1_1_927
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 2|(5x^2 + 5x - 3) + 1| - 1, g(x) = -5x - 4, x = -1.6, and x = -1.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.8
|
math
|
train
| 927 |
math_algebra_func_area_level_1_1_928
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3sin(1π(2x^2 - 2) + 1) - 1 and g(x) = -2|x + 2| + 1 between the vertical lines x = -2.8 and x = -2.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
train
| 928 |
math_algebra_func_area_level_1_1_929
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1(-2|x - 3|)^2 + 3(-2|x - 3|) + 3 and g(x) = (-3x - 1)/(3x + 2) from x = 2.5 to x = 3.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.1
|
math
|
train
| 929 |
math_algebra_func_area_level_1_1_930
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(4x^2 - 4x - 3)^2 + 4(4x^2 - 4x - 3) + 2 and g(x) = (-2x + 2)/(-3x - 1) between the vertical lines x = -0.6 and x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
20.2
|
math
|
train
| 930 |
math_algebra_func_area_level_1_1_931
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 4(-3x + 1)^2 + 4(-3x + 1) - 3 and g(x) = 2|x| - 3 between the vertical lines x = 0.3 and x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.7
|
math
|
train
| 931 |
math_algebra_func_area_level_1_1_932
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (3(3sin(3πx + 2)))/(1(3sin(3πx + 2)) + 1) and g(x) = (2x)/(-1x - 1) from x = 3.5 to x = 3.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.3
|
math
|
train
| 932 |
math_algebra_func_area_level_1_1_933
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -3cos(3π((-2x - 1)/(1x - 2)) + 3) + 3, g(x) = 4x^2 - 2x - 4, x = 1.6, and x = 1.7000000000000002. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.2
|
math
|
train
| 933 |
math_algebra_func_area_level_1_1_934
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 4(-3sin(1πx - 2) + 1) + 2 and g(x) = -2|x - 2| + 3 from x = 2.8 to x = 3.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.1
|
math
|
train
| 934 |
math_algebra_func_area_level_1_1_935
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(2sin(2πx + 3) + 2)^2 - 1(2sin(2πx + 3) + 2) - 3 and g(x) = -1x^2 - 5x between the vertical lines x = -0.0 and x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.8
|
math
|
train
| 935 |
math_algebra_func_area_level_1_1_936
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2sin(2π((1x - 2)/(2x - 3)) - 3) + 1 and g(x) = 1|x + 1| between the vertical lines x = 1.4 and x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.2
|
math
|
train
| 936 |
math_algebra_func_area_level_1_1_937
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -5(3cos(2πx - 3) - 3) + 2, g(x) = 2x^2 - 2x + 5, x = -2.2, and x = -1.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.5
|
math
|
train
| 937 |
math_algebra_func_area_level_1_1_938
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -4(-5x^2 - 2x + 1) + 4 and g(x) = -5x^2 - 3x between the vertical lines x = -0.4 and x = 0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.3
|
math
|
train
| 938 |
math_algebra_func_area_level_1_1_939
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (1(-1x + 3) - 3)/(3(-1x + 3) - 1), g(x) = 1x^2 - 5x + 2, x = 2.5, and x = 4.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
48.7
|
math
|
train
| 939 |
math_algebra_func_area_level_1_1_940
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2cos(2π(-3|x - 2| + 3) - 3) + 3 and g(x) = 2x + 5 between the vertical lines x = -1.7 and x = -1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
math
|
train
| 940 |
math_algebra_func_area_level_1_1_941
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -2cos(1π(2|x| + 3) - 1) - 3 and g(x) = (3x + 3)/(-3x + 2) from x = 2.3 to x = 3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.3
|
math
|
train
| 941 |
math_algebra_func_area_level_1_1_942
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(-3cos(3πx + 2) + 1))/(-3(-3cos(3πx + 2) + 1) + 1) and g(x) = -3|x - 2| + 2 between the vertical lines x = 0.3 and x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.9
|
math
|
train
| 942 |
math_algebra_func_area_level_1_1_943
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3(1sin(2πx + 1) - 1) - 5 and g(x) = -3x^2 + 1x - 2 between the vertical lines x = -1.5 and x = -1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.5
|
math
|
train
| 943 |
math_algebra_func_area_level_1_1_944
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 5(-3sin(2πx) + 3)^2 + 5(-3sin(2πx) + 3) - 3 and g(x) = -3|x + 1| - 2 between the vertical lines x = -0.8 and x = -0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
math
|
train
| 944 |
math_algebra_func_area_level_1_1_945
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(-1cos(2πx + 2) - 1) + 2 and g(x) = 3x^2 + 5x + 5 between the vertical lines x = -1.4 and x = -1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
train
| 945 |
math_algebra_func_area_level_1_1_946
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (2(3sin(1πx - 1)) - 3)/(3(3sin(1πx - 1)) + 1) and g(x) = 2|x + 2| + 1 from x = -0.6 to x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.8
|
math
|
train
| 946 |
math_algebra_func_area_level_1_1_947
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (3(-3x^2 + 2x))/(-1(-3x^2 + 2x) + 2), g(x) = -1|x - 3| - 1, x = 1.8, and x = 4.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.8
|
math
|
train
| 947 |
math_algebra_func_area_level_1_1_948
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1((2x + 1)/(1x))^2 - 2 and g(x) = -3|x - 1| - 3 between the vertical lines x = -0.2 and x = 2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5.3
|
math
|
train
| 948 |
math_algebra_func_area_level_1_1_949
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(2|x + 1| + 1) - 1)/(3(2|x + 1| + 1) + 3) and g(x) = 1x^2 + 1x - 3 between the vertical lines x = -2.1 and x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5.8
|
math
|
train
| 949 |
math_algebra_func_area_level_1_1_950
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -2cos(2π(-1x + 3) - 3) - 1 and g(x) = (3x + 2)/(-2x + 3) from x = -1.8 to x = -1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.0
|
math
|
train
| 950 |
math_algebra_func_area_level_1_1_951
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1sin(3π(-1|x - 3| - 3) - 1) - 3 and g(x) = -1x^2 + 5x - 5 from x = 0.2 to x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
train
| 951 |
math_algebra_func_area_level_1_1_952
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3e^(-2(1x + 2)) - 1 and g(x) = -5x^2 + 3 between the vertical lines x = -0.9 and x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.6
|
math
|
train
| 952 |
math_algebra_func_area_level_1_1_953
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1cos(1π(-3x - 1) - 2) - 2 and g(x) = -1x + 2 from x = 4.3 to x = 4.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.4
|
math
|
train
| 953 |
math_algebra_func_area_level_1_1_954
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1|(-2cos(3πx - 2) - 2) - 2| + 1 and g(x) = -1|x - 2| + 2 from x = -2.0 to x = -1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.9
|
math
|
train
| 954 |
math_algebra_func_area_level_1_1_955
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3|(1x - 5) + 2| - 2 and g(x) = (3x)/(3x + 2) between the vertical lines x = -0.8 and x = 2.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
30.7
|
math
|
train
| 955 |
math_algebra_func_area_level_1_1_956
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(-1sin(2πx - 3) - 2) + 1)/(-2(-1sin(2πx - 3) - 2) - 1) and g(x) = -3x^2 + 1x + 2 between the vertical lines x = -1.0 and x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5.8
|
math
|
train
| 956 |
math_algebra_func_area_level_1_1_957
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2cos(1π((2x - 2)/(1x + 2)) + 2) + 1 and g(x) = (2x - 2)/(-3x - 2) between the vertical lines x = -0.4 and x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
train
| 957 |
math_algebra_func_area_level_1_1_958
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3sin(2π(-1x - 5) + 1) - 2 and g(x) = 3|x - 3| - 2 from x = 3.2 to x = 3.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.5
|
math
|
train
| 958 |
math_algebra_func_area_level_1_1_959
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 4((-2x - 1)/(-2x + 1))^2 + 3((-2x - 1)/(-2x + 1)) - 3 and g(x) = 3|x - 2| from x = 0.2 to x = 4.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
11.6
|
math
|
train
| 959 |
math_algebra_func_area_level_1_1_960
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -2sin(3π((2x + 3)/(1x - 2)) - 2) - 2 and g(x) = (2x + 2)/(3x - 2) from x = -0.6 to x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.9
|
math
|
train
| 960 |
math_algebra_func_area_level_1_1_961
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 3|(-3x^2 + 4x + 3) + 1| - 2 and g(x) = (-3x + 2)/(3x - 2) 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"
}
] |
0.1
|
math
|
train
| 961 |
math_algebra_func_area_level_1_1_962
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3(-3x^2 + 4) + 3)/(-1(-3x^2 + 4) - 3) and g(x) = -2x^2 + 1x - 2 between the vertical lines x = -1.4 and x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
9.5
|
math
|
train
| 962 |
math_algebra_func_area_level_1_1_963
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1sin(3π(1|x - 2| + 3)) + 2, g(x) = 4x^2 - 4x - 1, x = -0.6, and x = 1.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5.4
|
math
|
train
| 963 |
math_algebra_func_area_level_1_1_964
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1sin(2π(-2x + 4) - 3) - 2 and g(x) = -3x + 3 between the vertical lines x = 1.4 and x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
math
|
train
| 964 |
math_algebra_func_area_level_1_1_965
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(1cos(2πx - 2) - 1)^2 - 5(1cos(2πx - 2) - 1) - 4 and g(x) = (2x)/(-1x - 2) between the vertical lines x = -4.8 and x = -4.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
train
| 965 |
math_algebra_func_area_level_1_1_966
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 2sin(3π(2x + 3) + 2), g(x) = 1x^2 - 4x + 1, x = 1.0, and x = 3.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5.9
|
math
|
train
| 966 |
math_algebra_func_area_level_1_1_967
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1|(-2x - 1) - 2| - 1 and g(x) = -1|x| + 2 from x = -2.0 to x = 0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1.5
|
math
|
train
| 967 |
math_algebra_func_area_level_1_1_968
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(-3|x + 3|)^2 + 2 and g(x) = -1x between the vertical lines x = -3.4 and x = -2.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.5
|
math
|
train
| 968 |
math_algebra_func_area_level_1_1_969
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -4(1x^2 + 2x) - 3, g(x) = 2x^2 + 1x - 1, x = -1.2, and x = -0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.9
|
math
|
train
| 969 |
math_algebra_func_area_level_1_1_970
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-1(-1cos(3πx + 3) + 3) - 1)/(2(-1cos(3πx + 3) + 3) - 3) and g(x) = -3|x| from x = -1.0 to x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.4
|
math
|
train
| 970 |
math_algebra_func_area_level_1_1_971
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-1((-2x - 2)/(-1x + 3)) - 1)/(-3((-2x - 2)/(-1x + 3)) + 4), g(x) = -1x^2 - 5x - 3, x = -4.8, and x = -0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
10.7
|
math
|
train
| 971 |
math_algebra_func_area_level_1_1_972
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (2(-2|x + 2| + 1))/(-3(-2|x + 2| + 1) - 2), g(x) = -1x^2 + 3x + 4, x = -2.8, and x = 4.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
43.5
|
math
|
train
| 972 |
math_algebra_func_area_level_1_1_973
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-1((3x + 3)/(3x + 1)) + 3)/(-1((3x + 3)/(3x + 1)) - 1), g(x) = 3x - 1, x = -0.9, and x = 0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
33.4
|
math
|
train
| 973 |
math_algebra_func_area_level_1_1_974
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3(4x^2 - 1x + 3) - 1)/(-1(4x^2 - 1x + 3) - 3) and g(x) = -2|x + 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{Your answer}",
"role": "user"
}
] |
0.3
|
math
|
train
| 974 |
math_algebra_func_area_level_1_1_975
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -3cos(1π(-3x^2 + 5x + 1) + 2) + 1, g(x) = -1x - 3, x = -1.6, and x = -1.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.3
|
math
|
train
| 975 |
math_algebra_func_area_level_1_1_976
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1(1sin(3πx + 3) - 2)^2 + 4(1sin(3πx + 3) - 2) - 5, g(x) = -2x^2 - 1x - 3, x = -2.0, and x = 1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
12.6
|
math
|
train
| 976 |
math_algebra_func_area_level_1_1_977
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3(2|x + 1| - 3) + 1, g(x) = 2|x - 1| + 2, x = -4.5, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
36.8
|
math
|
train
| 977 |
math_algebra_func_area_level_1_1_978
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2sin(3π(-3x^2 + 1x - 5) - 1) + 2 and g(x) = 4x^2 - 1x - 3 from x = 1.3 to x = 1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.2
|
math
|
train
| 978 |
math_algebra_func_area_level_1_1_979
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (1(-3sin(2πx + 1) + 1) - 3)/(-2(-3sin(2πx + 1) + 1) - 2), g(x) = 2x + 5, x = -4.0, and x = -3.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
math
|
train
| 979 |
math_algebra_func_area_level_1_1_980
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 2|(-1x^2 + 3x + 5)| - 3, g(x) = (3x)/(1x + 2), x = 3.7, and x = 4.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.4
|
math
|
train
| 980 |
math_algebra_func_area_level_1_1_981
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(-4x - 3) + 1)/(-2(-4x - 3) - 2) and g(x) = 5x + 5 between the vertical lines x = -1.0 and x = -0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
12.3
|
math
|
train
| 981 |
math_algebra_func_area_level_1_1_982
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (3(-3sin(2πx) + 2) + 3)/(1(-3sin(2πx) + 2) - 3) and g(x) = (-3x)/(1x - 2) from x = -1.6 to x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
16.1
|
math
|
train
| 982 |
math_algebra_func_area_level_1_1_983
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-1(-3e^(1x)))/(1(-3e^(1x)) + 1) and g(x) = 3x^2 - 2x - 2 from x = -0.2 to x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.8
|
math
|
train
| 983 |
math_algebra_func_area_level_1_1_984
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -4(2x^2 + 2x - 2)^2 - 3(2x^2 + 2x - 2) + 5 and g(x) = -4x from x = 0.2 to x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.4
|
math
|
train
| 984 |
math_algebra_func_area_level_1_1_985
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3(3sin(1πx - 2))^2 + 2(3sin(1πx - 2)) - 4 and g(x) = (2x + 3)/(-2x + 3) between the vertical lines x = -4.2 and x = -3.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
7.1
|
math
|
train
| 985 |
math_algebra_func_area_level_1_1_986
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(1x + 3) - 1 and g(x) = (1x - 3)/(3x - 2) between the vertical lines x = -4.5 and x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
43.5
|
math
|
train
| 986 |
math_algebra_func_area_level_1_1_987
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2|((3x - 3)/(-3x)) + 2| + 1, g(x) = -1|x - 3|, x = -0.3, and x = 4.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
25.2
|
math
|
train
| 987 |
math_algebra_func_area_level_1_1_988
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1(-3sin(2πx + 3) + 2) + 3, g(x) = 2|x - 2| - 1, x = 3.6, and x = 3.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.3
|
math
|
train
| 988 |
math_algebra_func_area_level_1_1_989
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1sin(1π(-1x^2 + 4x + 4) - 3) - 2 and g(x) = 1x^2 + 3x - 2 from x = -2.6 to x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.1
|
math
|
train
| 989 |
math_algebra_func_area_level_1_1_990
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (1(-4x^2 + 2x + 2) - 3)/(-1(-4x^2 + 2x + 2) - 2) and g(x) = -1x + 1 from x = -0.5 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.6
|
math
|
train
| 990 |
math_algebra_func_area_level_1_1_991
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-2(1|x + 2| - 2) + 3)/(3(1|x + 2| - 2) - 1) and g(x) = 2x - 1 from x = -0.4 to x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
15.0
|
math
|
train
| 991 |
math_algebra_func_area_level_1_1_992
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -3|(1cos(1πx - 1) + 1) + 3| - 2, g(x) = -5x^2 - 3x, x = -2.1, and x = 1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
33.6
|
math
|
train
| 992 |
math_algebra_func_area_level_1_1_993
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1|(2cos(2πx + 1)) + 2| + 1, g(x) = (1x - 3)/(-1x), x = -3.3, and x = -3.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.2
|
math
|
train
| 993 |
math_algebra_func_area_level_1_1_994
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (2(-1cos(2πx + 2) + 2) - 3)/(-1(-1cos(2πx + 2) + 2) + 2) and g(x) = (-1x + 1)/(3x - 2) from x = -2.5 to x = -2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.1
|
math
|
train
| 994 |
math_algebra_func_area_level_1_1_995
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3(2sin(3πx) + 1) + 2, g(x) = (-2x - 3)/(-2x + 3), x = 4.0, and x = 4.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2.3
|
math
|
train
| 995 |
math_algebra_func_area_level_1_1_996
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2(4x^2 - 1) + 2, g(x) = 5x + 1, x = -1.0, and x = 0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3.5
|
math
|
train
| 996 |
math_algebra_func_area_level_1_1_997
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(3sin(1πx - 3))^2 + 2(3sin(1πx - 3)) - 5 and g(x) = -1x^2 - 1x between the vertical lines x = -0.2 and x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4.2
|
math
|
train
| 997 |
math_algebra_func_area_level_1_1_998
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -4(-2x^2 - 2x + 4)^2 - 2(-2x^2 - 2x + 4) - 2, g(x) = -1x^2 + 3x + 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": "user"
}
] |
2.3
|
math
|
train
| 998 |
math_algebra_func_area_level_1_1_999
|
algebra_func_area1
|
easy (level 1)
| 1 |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1|(-1sin(2πx + 2) - 1) + 2| - 2 and g(x) = -2|x - 1| from x = -0.2 to x = -0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0.0
|
math
|
train
| 999 |
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