messages listlengths 1 1 | ground_truth stringlengths 1 3 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Find the total number of local minima and maxima for f(x) = (2(3|(1((-1(1x^2 - 4x + 3) - 2)/(3(1x^2 - 4x + 3) - 1))^2 - 5((-1(1x^2 - 4x + 3) - 2)/(3(1x^2 - 4x + 3) - 1)) - 4) - 2| - 2) - 2)/(2(3|(1((-1(1x^2 - 4x + 3) - 2)/(3(1x^2 - 4x + 3) - 1))^2 - 5((-1(1x^2 - 4x + 3) - 2)/(3(1x^2 - 4x + 3) - 1)... | 9 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = -4((3(-5(-3sin(2π((-2x + 3)/(-1x + 2)) + 3) - 2)^2 - 5(-3sin(2π((-2x + 3)/(-1x + 2)) + 3) - 2) + 4) + 2)/(-1(-5(-3sin(2π((-2x + 3)/(-1x + 2)) + 3) - 2)^2 - 5(-3sin(2π((-2x + 3)/(-1x + 2)) + 3) - 2) + 4) - 1)) - 2 where -10 ≤ x ≤ 10.\n\nPr... | 35 | MATH |
[
{
"content": "How many local maxima does the function f(x) = 1(-2|(3(2e^(-1(-5x)) + 2) - 4)| - 2) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = 3(-2(-1(2e^(1(-1x^2 - 5x + 2)) + 1)^2 + 3(2e^(1(-1x^2 - 5x + 2)) + 1) + 2)^2 + 4(-1(2e^(1(-1x^2 - 5x + 2)) + 1)^2 + 3(2e^(1(-1x^2 - 5x + 2)) + 1) + 2) - 3)^2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 7 | MATH |
[
{
"content": "How many local maxima does the function f(x) = 1|(3sin(2π(-3|((3(1x^2 - 5) + 1)/(-1(1x^2 - 5) + 2)) - 2| - 3) - 3) - 2) + 3| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 133 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = -2|(-1((1(-1(2cos(1πx + 2) - 3)^2 + 4(2cos(1πx + 2) - 3) - 5) - 2)/(-1(-1(2cos(1πx + 2) - 3)^2 + 4(2cos(1πx + 2) - 3) - 5) - 3)) - 2) - 3| - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your an... | 20 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = -4(-1|(1|(-3(2x^2 - 3)^2 - 1(2x^2 - 3)) + 2| - 2) - 3| - 1) + 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1e^(1(-5((3(-1|(-2|x - 1| + 2) + 3| + 2) + 1)/(-2(-1|(-2|x - 1| + 2) + 3| + 2) + 3)))) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "How many local maxima does the function f(x) = 4(2e^(1(-3(1|(-1x) - 2| - 2)^2 - 5(1|(-1x) - 2| - 2) + 5))) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = 2(1(1cos(1π(-5(-1x^2 + 2x + 4) + 3)) + 1)^2 - 3(1cos(1π(-5(-1x^2 + 2x + 4) + 3)) + 1) - 3) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 476 | MATH |
[
{
"content": "How many local minima does the function f(x) = -2|(-4(5(3|(1cos(1πx) - 3) + 2| - 2)^2 - 3)^2 - 4(5(3|(1cos(1πx) - 3) + 2| - 2)^2 - 3) - 5) - 1| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = 5(2cos(1π(-5(-2(-5x - 1)^2 + 4(-5x - 1) - 1) + 2) - 3)) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 163 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1|(-1|(3|((-3(-2sin(3πx - 1) + 3) + 2)/(-1(-2sin(3πx - 1) + 3))) + 3| + 1) + 2| - 2)| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = (2(-1|((1(-2cos(2π(5x + 4) - 3) + 1) + 2)/(-3(-2cos(2π(5x + 4) - 3) + 1) - 2)) - 3| - 2) - 3)/(3(-1|((1(-2cos(2π(5x + 4) - 3) + 1) + 2)/(-3(-2cos(2π(5x + 4) - 3) + 1) - 2)) - 3| - 2) - 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: ... | 56 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = 1(1sin(2π(-3((-2(-2|x - 2| + 2) + 3)/(-2(-2|x - 2| + 2) - 3))^2 + 2((-2(-2|x - 2| + 2) + 3)/(-2(-2|x - 2| + 2) - 3)) + 4) - 2)) - 5 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 75 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = (2(1((-3(-3cos(2π(1x + 3)) - 2) + 2)/(3(-3cos(2π(1x + 3)) - 2) - 1))^2 + 3((-3(-3cos(2π(1x + 3)) - 2) + 2)/(3(-3cos(2π(1x + 3)) - 2) - 1)) - 2) - 2)/(1(1((-3(-3cos(2π(1x + 3)) - 2) + 2)/(3(-3cos(2π(1x + 3)) - 2) - 1))^2 + 3(... | 119 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = -3((2(1|(-1(-1cos(3πx + 1) + 1) + 4)| + 1) + 2)/(2(1|(-1(-1cos(3πx + 1) + 1) + 4)| + 1) + 3))^2 + 4((2(1|(-1(-1cos(3πx + 1) + 1) + 4)| + 1) + 2)/(2(1|(-1(-1cos(3πx + 1) + 1) + 4)| + 1) + 3)) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex f... | 30 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = -2sin(1π(3(-5(4((2x + 3)/(-2x + 3))^2 + 1((2x + 3)/(-2x + 3)) + 1)^2) + 5) + 2) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 139 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = -4(1(-3(-1sin(2π((-2x - 1)/(3x - 2)) + 2) + 1)^2 + 4(-1sin(2π((-2x - 1)/(3x - 2)) + 2) + 1) + 4)^2 - 3(-3(-1sin(2π((-2x - 1)/(3x - 2)) + 2) + 1)^2 + 4(-1sin(2π((-2x - 1)/(3x - 2)) + 2) + 1) + 4) + 4) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer i... | 23 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = -4(-1cos(1π(-1|(-1|(-1|x| + 3) + 2| + 1) + 2| - 3) + 3) - 2)^2 + 2(-1cos(1π(-1|(-1|(-1|x| + 3) + 2| + 1) + 2| - 3) + 3) - 2) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 27 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2(-3(3(3|(3sin(2πx - 2) + 3) + 3| + 3) + 5)^2 - 2(3(3|(3sin(2πx - 2) + 3) + 3| + 3) + 5) - 5)^2 + 1(-3(3(3|(3sin(2πx - 2) + 3) + 3| + 3) + 5)^2 - 2(3(3|(3sin(2πx - 2) + 3) + 3| + 3) + 5) - 5) + 3 have in the interval [-10... | 32 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = (-2(-2|((1(5(-5x^2 - 4x + 3)^2 - 1(-5x^2 - 4x + 3) - 5) + 3)/(-1(5(-5x^2 - 4x + 3)^2 - 1(-5x^2 - 4x + 3) - 5) + 2)) + 1| - 2) - 1)/(-1(-2|((1(5(-5x^2 - 4x + 3)^2 - 1(-5x^2 - 4x + 3) - 5) + 3)/(-1(5(-5x^2 - 4x + 3)^2 - 1(-5x^2 - 4x + 3) - 5) + 2)) ... | 7 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = (-1((-1(3(-3cos(1π((-3x + 1)/(1x + 1)) + 1) - 1)) - 2)/(2(3(-3cos(1π((-3x + 1)/(1x + 1)) + 1) - 1)) + 3)) + 1)/(-2((-1(3(-3cos(1π((-3x + 1)/(1x + 1)) + 1) - 1)) - 2)/(2(3(-3cos(1π((-3x + 1)/(1x + 1)) + 1) - 1)) + 3)) - 2) where -10 ≤ x ≤ ... | 43 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = -1|(-3|(-4(1(-2sin(3πx + 2) - 1)^2 + 2(-2sin(3πx + 2) - 1) - 5) + 2) + 1|) + 1| + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "How many local maxima does the function f(x) = 2(-4(4((2(1cos(3πx - 2) - 2) + 2)/(-3(1cos(3πx - 2) - 2) + 2)) + 2)^2 + 4(4((2(1cos(3πx - 2) - 2) + 2)/(-3(1cos(3πx - 2) - 2) + 2)) + 2) + 4) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 30 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = (-3((2(-1((-1(-2cos(1πx + 2) - 1) + 1)/(3(-2cos(1πx + 2) - 1) + 2)) + 1) - 1)/(-3(-1((-1(-2cos(1πx + 2) - 1) + 1)/(3(-2cos(1πx + 2) - 1) + 2)) + 1) + 1)) + 1)/(1((2(-1((-1(-2cos(1πx + 2) - 1) + 1)/(3(-2cos(1πx + 2) - 1) + 2)) + 1) - 1)/(-... | 20 | MATH |
[
{
"content": "How many local minima does the function f(x) = -1|(2cos(2π(2|(3|(-4x - 1) + 3| - 2) - 2| - 1))) - 2| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 482 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = -1(2|(-2|(-4((1x)/(2x - 1)) + 4) + 2| + 2) - 1| + 3)^2 + 2(2|(-2|(-4((1x)/(2x - 1)) + 4) + 2| + 2) - 1| + 3) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 4 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = (3(2sin(2π(1|(-5((1x - 3)/(-1x + 2))^2 + 2((1x - 3)/(-1x + 2)) + 2)| + 1)) - 1) - 1)/(-1(2sin(2π(1|(-5((1x - 3)/(-1x + 2))^2 + 2((1x - 3)/(-1x + 2)) + 2)| + 1)) - 1) - 2) in the interval [-10, 10].\n\nPresent the answer in L... | 78 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = (3((-2((2((-3(1|x + 2| + 1) + 2)/(-1(1|x + 2| + 1) + 3)) + 1)/(-3((-3(1|x + 2| + 1) + 2)/(-1(1|x + 2| + 1) + 3)) - 1)) - 2)/(1((2((-3(1|x + 2| + 1) + 2)/(-1(1|x + 2| + 1) + 3)) + 1)/(-3((-3(1|x + 2| + 1) + 2)/(-1(1|x + 2| + ... | 290 | MATH |
[
{
"content": "How many local minima does the function f(x) = 2cos(2π(-2|(2(-2(2x^2 + 1x + 1) + 5) + 5) + 2| + 1) - 3) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 241 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = (2(5(4(-3|(-1sin(2πx - 1) + 3) + 1| + 2)^2 + 1(-3|(-1sin(2πx - 1) + 3) + 1| + 2) + 2) - 2) + 2)/(1(5(4(-3|(-1sin(2πx - 1) + 3) + 1| + 2)^2 + 1(-3|(-1sin(2πx - 1) + 3) + 1| + 2) + 2) - 2) + 3) in the interval [-10, 10].\n\nPr... | 40 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = -1(-3((2(3sin(3π(2|x + 3| - 3) - 2)) + 3)/(2(3sin(3π(2|x + 3| - 3) - 2)) + 1))^2 - 4((2(3sin(3π(2|x + 3| - 3) - 2)) + 3)/(2(3sin(3π(2|x + 3| - 3) - 2)) + 1)) - 3) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\box... | 160 | MATH |
[
{
"content": "How many local maxima does the function f(x) = 2(3cos(2π(-4(-5(1x + 1)^2 + 5(1x + 1) + 5)^2 + 3) - 3) + 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 53 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = 3sin(1π(2|(-2|(-5(2x + 4)^2 - 2(2x + 4) + 5) + 3| - 2) + 3| - 1)) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 447 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1sin(3π(-4(5(-1|(-4x^2 - 2x + 1) - 3| + 3)^2 + 1(-1|(-4x^2 - 2x + 1) - 3| + 3)) + 5) - 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 99 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = 3cos(3π(-2|(-1|(3(1x^2 - 3x) - 3) - 1| - 3) + 3| + 3) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 484 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = (1(3(-2(-2e^(2(5x^2 - 1x)) - 2) - 4) - 4) - 1)/(3(3(-2(-2e^(2(5x^2 - 1x)) - 2) - 4) - 4) + 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 29 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = -1|(-5(-2cos(1π(5(-4x - 3)^2 + 2(-4x - 3) + 2) + 2) - 3) + 5) + 1| - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 211 | MATH |
[
{
"content": "How many local minima does the function f(x) = -2(-5(-3sin(2π(1(1x - 2) - 2) + 1))^2 + 1(-3sin(2π(1(1x - 2) - 2) + 1)) - 3) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = (2(1(-2|(-3sin(2π(4x^2 - 3x + 4) - 3) - 3)| + 1)^2 + 2(-2|(-3sin(2π(4x^2 - 3x + 4) - 3) - 3)| + 1) - 4) - 2)/(-3(1(-2|(-3sin(2π(4x^2 - 3x + 4) - 3) - 3)| + 1)^2 + 2(-2|(-3sin(2π(4x^2 - 3x + 4) - 3) - 3)| + 1) - 4) + 1) in th... | 501 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = 5((2(-5(-1(2cos(3πx + 2) - 3)^2 - 2(2cos(3πx + 2) - 3) - 4)^2 - 2(-1(2cos(3πx + 2) - 3)^2 - 2(2cos(3πx + 2) - 3) - 4) + 3) - 1)/(1(-5(-1(2cos(3πx + 2) - 3)^2 - 2(2cos(3πx + 2) - 3) - 4)^2 - 2(-1(2cos(3πx + 2) - 3)^2 - 2(2cos(3πx + 2) - 3)... | 30 | MATH |
[
{
"content": "How many local maxima does the function f(x) = (-1(-3|(-2sin(1π(2((-3x - 1)/(1x - 2))^2 - 1((-3x - 1)/(1x - 2))) + 1) + 2) - 2| - 1) - 2)/(-1(-3|(-2sin(1π(2((-3x - 1)/(1x - 2))^2 - 1((-3x - 1)/(1x - 2))) + 1) + 2) - 2| - 1)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\... | 208 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = -1(3|(-5(1|(-3|x + 2| + 2) + 3| - 1)^2 + 1(1|(-3|x + 2| + 2) + 3| - 1) + 4) + 2|) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = (1(-1|(5(1e^(1(-5x - 4)) + 2)^2 - 4(1e^(1(-5x - 4)) + 2) + 3)| - 1) + 1)/(1(-1|(5(1e^(1(-5x - 4)) + 2)^2 - 4(1e^(1(-5x - 4)) + 2) + 3)| - 1) - 3) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 14 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = 1(-4(1|(3(-1|x| + 3)^2 - 4) - 3|) - 5) + 5 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = 3|(-5(-4(-3sin(2π(-2x - 3) + 2) + 3) - 4) + 2)| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "How many local minima does the function f(x) = 1(2cos(1π(-4(-1(-2x^2 + 3x + 2)^2 + 2(-2x^2 + 3x + 2) + 5)^2 - 3(-1(-2x^2 + 3x + 2)^2 + 2(-2x^2 + 3x + 2) + 5)) + 1) - 2) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 47 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = 2(4((-3((-3((2x - 1)/(1x + 2)) - 3)/(-1((2x - 1)/(1x + 2)))))/(-1((-3((2x - 1)/(1x + 2)) - 3)/(-1((2x - 1)/(1x + 2))))))^2 - 1((-3((-3((2x - 1)/(1x + 2)) - 3)/(-1((2x - 1)/(1x + 2)))))/(-1((-3((2x - 1)/(1x + 2)) - 3)/(-1((2x - 1)/(1x + 2)))))) + 5... | 125 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = 2(-3sin(3π((1(-1(4x + 5) - 1) + 1)/(-3(-1(4x + 5) - 1) + 4)) + 3) + 1)^2 + 2(-3sin(3π((1(-1(4x + 5) - 1) + 1)/(-3(-1(4x + 5) - 1) + 4)) + 3) + 1) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",... | 9 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = 1(1|(-5(3|(4x^2 + 5x) + 1| - 1) - 5) + 3| - 2) + 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "How many local minima does the function f(x) = 3(-1cos(1π((1(-3|((3x - 2)/(1x + 2)) - 2| + 3) - 3)/(1(-3|((3x - 2)/(1x + 2)) - 2| + 3))) + 1) + 3) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 17 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = 3(-1|(-1|(-1(1x^2 + 5x + 3)^2 + 1(1x^2 + 5x + 3) + 1) - 1| + 1) + 3| + 2) - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9 | MATH |
[
{
"content": "How many local maxima does the function f(x) = (1(5(-1|(-2(1e^(-2x) + 1)) + 2| - 2)^2 - 1(-1|(-2(1e^(-2x) + 1)) + 2| - 2) + 1) + 3)/(3(5(-1|(-2(1e^(-2x) + 1)) + 2| - 2)^2 - 1(-1|(-2(1e^(-2x) + 1)) + 2| - 2) + 1) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Yo... | 36 | MATH |
[
{
"content": "How many local minima does the function f(x) = 4(1|(1sin(3π(-2(-1x^2 + 1x - 3) - 4) + 1) - 3) - 2| + 3)^2 + 3(1|(1sin(3π(-2(-1x^2 + 1x - 3) - 4) + 1) - 3) - 2| + 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 235 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = -3|(-2|(1sin(1π(-5(-2x^2 - 1x - 3)^2 + 1(-2x^2 - 1x - 3) + 4) - 3) - 1) - 1| - 3) - 2| + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 111 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = 2cos(2π(-3(-1(5(-1x^2 - 1x + 5)^2 - 4(-1x^2 - 1x + 5) + 1))^2 - 5(-1(5(-1x^2 - 1x + 5)^2 - 4(-1x^2 - 1x + 5) + 1)) - 4) + 2) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 34 | MATH |
[
{
"content": "How many local minima does the function f(x) = 1cos(2π(2|(-1|(5(-2|x - 3| - 3) - 1) - 3| - 3) + 3| + 1) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 401 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = 1cos(1π(-1(-1(5((2x - 1)/(2x + 3))^2 - 3((2x - 1)/(2x + 3)) - 4)^2 + 2(5((2x - 1)/(2x + 3))^2 - 3((2x - 1)/(2x + 3)) - 4) + 1) + 5) - 1) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 142 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = -2|(1(4((3(1cos(3πx) - 3))/(3(1cos(3πx) - 3) - 1)) - 3) + 5) + 3| + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = 4(1(2(-3sin(1π(-2|x + 3|) - 2) + 2) + 2) + 5) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1(-2|(-3sin(2π(2((-2x - 3)/(-2x - 2))^2 + 2((-2x - 3)/(-2x - 2)) + 2) + 1) - 2) + 1| + 1)^2 - 5(-2|(-3sin(2π(2((-2x - 3)/(-2x - 2))^2 + 2((-2x - 3)/(-2x - 2)) + 2) + 1) - 2) + 1| + 1) have in the interval [-10, 10]?\n\nPr... | 59 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = -3|(3(3sin(2π(1(3|x + 2|)^2 - 5(3|x + 2|) - 2) - 1) - 1) - 3) + 1| - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = 1((3((1(-2sin(3π(1x - 5) + 2) - 2) - 3)/(2(-2sin(3π(1x - 5) + 2) - 2) + 2)) + 2)/(1((1(-2sin(3π(1x - 5) + 2) - 2) - 3)/(2(-2sin(3π(1x - 5) + 2) - 2) + 2)))) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{You... | 30 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = 3cos(3π(-1((-2(1|(1x - 3) - 1| - 1) - 3)/(1(1|(1x - 3) - 1| - 1) + 1))^2 + 3((-2(1|(1x - 3) - 1| - 1) - 3)/(1(1|(1x - 3) - 1| - 1) + 1))) - 2) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{You... | 96 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = (1(-4(-2((-3((3x)/(-3x - 3)))/(-2((3x)/(-3x - 3)))) + 2)^2 + 5))/(1(-4(-2((-3((3x)/(-3x - 3)))/(-2((3x)/(-3x - 3)))) + 2)^2 + 5) + 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 117 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = 2((-3(1sin(2π((3(-1|x + 2| - 2) + 2)/(-2(-1|x + 2| - 2) - 3)) - 3) + 3))/(1(1sin(2π((3(-1|x + 2| - 2) + 2)/(-2(-1|x + 2| - 2) - 3)) - 3) + 3) + 1))^2 + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answe... | 6 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = (-2(3cos(3π(4(3|(-5x - 1) + 2| - 2)^2 + 2(3|(-5x - 1) + 2| - 2) - 4) + 1) - 1))/(3(3cos(3π(4(3|(-5x - 1) + 2| - 2)^2 + 2(3|(-5x - 1) + 2| - 2) - 4) + 1) - 1) - 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 113 | MATH |
[
{
"content": "How many local maxima does the function f(x) = -3cos(1π(-2|(-1(3(-4x^2 - 4x - 4) - 3) - 3) + 1| + 3) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 238 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = -5(5(-3cos(2π(3(-5x^2 + 2) + 1) - 3)) - 2) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 223 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = -3|(1((-2((3(-2sin(3πx + 1) - 2) - 2)/(-1(-2sin(3πx + 1) - 2) + 2)) + 3)/(-2((3(-2sin(3πx + 1) - 2) - 2)/(-1(-2sin(3πx + 1) - 2) + 2)) + 1))^2 + 3((-2((3(-2sin(3πx + 1) - 2) - 2)/(-1(-2sin(3πx + 1) - 2) + 2)) + 3)/(-2((3(-2sin(3πx + 1) - ... | 30 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = -1cos(3π(1(-2(1|(3|x + 2| + 2) + 1|)^2 + 4(1|(3|x + 2| + 2) + 1|) + 3) + 5)) - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 475 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = -1(2|(-1cos(1π(1|(-2x - 2) + 3| - 1) - 2) + 3)| - 3) + 4 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = -3sin(3π(1((-3(-5(-4x - 3) + 2) - 1)/(1(-5(-4x - 3) + 2) + 2)) - 4) - 3) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = 1|(1(2|(5(-2|x - 3| + 1)^2 + 4(-2|x - 3| + 1) - 5)| + 3) + 4) + 3| - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = 3(1|(3|(1cos(3π(-3|x + 3| - 3) - 3) + 1) - 3| - 2) + 2| + 2)^2 - 1(1|(3|(1cos(3π(-3|x + 3| - 3) - 3) + 1) - 3| - 2) + 2| + 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 90 | MATH |
[
{
"content": "How many local maxima does the function f(x) = -3|(-5(-2(3|((2x + 3)/(3x - 1)) - 2|)^2 + 1(3|((2x + 3)/(3x - 1)) - 2|) - 3)^2 - 5) + 1| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many local minima does the function f(x) = -2|(-2(-3((-1(-3cos(1πx - 2) - 2) - 2)/(-2(-3cos(1πx - 2) - 2) - 1))^2 + 3) - 3) + 3| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 49 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1(-2(4(-2|(-1sin(3πx) + 2) + 3| + 3) + 4) + 3)^2 - 3(-2(4(-2|(-1sin(3πx) + 2) + 3| + 3) + 4) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "How many local minima does the function f(x) = 3sin(2π(1(2|(3((-2x + 1)/(-3x))^2 + 4((-2x + 1)/(-3x)))|)) - 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 35 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = -5((-3(3|(1cos(3π(-1x^2 - 1x + 3) + 2) - 3) + 1| - 2) - 3)/(-3(3|(1cos(3π(-1x^2 - 1x + 3) + 2) - 3) + 1| - 2) - 1)) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 566 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = -3(2|(-3cos(1π(-2|(2|x - 1| - 3) + 1| + 1) - 1) + 3) + 2| - 3)^2 + 3(2|(-3cos(1π(-2|(2|x - 1| - 3) + 1| + 1) - 1) + 3) + 2| - 3) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 42 | MATH |
[
{
"content": "How many local minima does the function f(x) = -2|(5(1cos(1π((-1(1x + 5) + 1)/(1(1x + 5))) + 1) + 2)^2 + 2(1cos(1π((-1(1x + 5) + 1)/(1(1x + 5))) + 1) + 2) - 1) + 3| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9 | MATH |
[
{
"content": "How many local minima does the function f(x) = 1(5(-3(-2cos(1π((1x)/(-2x - 2)) - 1) - 1)^2 - 5(-2cos(1π((1x)/(-2x - 2)) - 1) - 1) + 1)^2 - 5) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 13 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = 4(-3|(-2cos(2π(2(-3|x + 2| - 1)^2 - 1(-3|x + 2| - 1) - 2) - 2) + 2) + 2| + 2) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 238 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = (-3(-1cos(1π(3|(-5(5x - 1) - 2) - 2| - 1) - 2) + 1) + 2)/(-2(-1cos(1π(3|(-5(5x - 1) - 2) - 2| - 1) - 2) + 1) + 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 250 | MATH |
[
{
"content": "How many local minima does the function f(x) = -1|(2(-2cos(2π(-3(-2x + 1) + 4) - 1) + 1)^2 + 5(-2cos(2π(-3(-2x + 1) + 4) - 1) + 1) - 2) - 3| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 479 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = (-3(-2(-1(2(-1cos(2πx + 1) + 1) - 4) + 2)^2 - 3(-1(2(-1cos(2πx + 1) + 1) - 4) + 2) - 2) - 3)/(3(-2(-1(2(-1cos(2πx + 1) + 1) - 4) + 2)^2 - 3(-1(2(-1cos(2πx + 1) + 1) - 4) + 2) - 2) + 1) in the interval [-10, 10].\n\nPresent the answer in L... | 20 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = 5(5(2(1(-5x^2 + 5x + 1)^2 - 2(-5x^2 + 5x + 1) - 2)^2 - 5(1(-5x^2 + 5x + 1)^2 - 2(-5x^2 + 5x + 1) - 2))^2 + 5(2(1(-5x^2 + 5x + 1)^2 - 2(-5x^2 + 5x + 1) - 2)^2 - 5(1(-5x^2 + 5x + 1)^2 - 2(-5x^2 + 5x + 1) - 2)) - 5) + 5 where -10 ≤ x ≤ 10.\n... | 9 | MATH |
[
{
"content": "How many local minima does the function f(x) = 1(-2sin(1π(4(1(-2x - 1)^2 + 2(-2x - 1) + 5)^2 - 4(1(-2x - 1)^2 + 2(-2x - 1) + 5) + 5) - 1) - 3) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 77 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = (3(-2sin(1π(5(-4(-3x + 2) + 2) + 3) - 2) - 2) + 2)/(2(-2sin(1π(5(-4(-3x + 2) + 2) + 3) - 2) - 2) - 3) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 797 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = -2((3(5(-2sin(3π(2|x + 1| + 2) - 2) + 1)^2 + 2(-2sin(3π(2|x + 1| + 2) - 2) + 1) - 4) + 2)/(-1(5(-2sin(3π(2|x + 1| + 2) - 2) + 1)^2 + 2(-2sin(3π(2|x + 1| + 2) - 2) + 1) - 4) + 3))^2 + 4((3(5(-2sin(3π(2|x + 1| + 2) - 2) + 1)^2... | 329 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2|(1((-3(-1e^(1(-5x - 4)) - 2) - 3)/(1(-1e^(1(-5x - 4)) - 2) + 2)) - 3) - 2| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16 | MATH |
[
{
"content": "How many local maxima does the function f(x) = 5(-4((1(2sin(2π((2x + 2)/(-2x + 3)) + 2) + 2) - 3)/(-3(2sin(2π((2x + 2)/(-2x + 3)) + 2) + 2) - 3))^2 - 4((1(2sin(2π((2x + 2)/(-2x + 3)) + 2) + 2) - 3)/(-3(2sin(2π((2x + 2)/(-2x + 3)) + 2) + 2) - 3)) + 2) + 5 have in the interval [-10, 10]?\n\nPresent ... | 27 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = (1((3(-2|(-3|((2x - 3)/(2x + 3)) + 2| - 3) + 2| - 1) + 3)/(-2(-2|(-3|((2x - 3)/(2x + 3)) + 2| - 3) + 2| - 1) - 2)) + 1)/(-2((3(-2|(-3|((2x - 3)/(2x + 3)) + 2| - 3) + 2| - 1) + 3)/(-2(-2|(-3|((2x - 3)/(2x + 3)) + 2| - 3) + 2| - 1) - 2)) + 1) where ... | 55 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = 1(-5(-1(4(-3sin(3πx - 1) + 2)^2 - 1(-3sin(3πx - 1) + 2) + 3)^2 + 4(4(-3sin(3πx - 1) + 2)^2 - 1(-3sin(3πx - 1) + 2) + 3) - 4)^2 - 3(-1(4(-3sin(3πx - 1) + 2)^2 - 1(-3sin(3πx - 1) + 2) + 3)^2 + 4(4(-3sin(3πx - 1) + 2)^2 - 1(-3sin(3πx - 1) + ... | 52 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1cos(3π(4((2((2(1x + 3) - 1)/(-2(1x + 3) + 3)) + 3)/(1((2(1x + 3) - 1)/(-2(1x + 3) + 3)) + 2))^2 - 5((2((2(1x + 3) - 1)/(-2(1x + 3) + 3)) + 3)/(1((2(1x + 3) - 1)/(-2(1x + 3) + 3)) + 2)) + 4) + 3) + 1 have in the interval... | 75 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = 2((3(3cos(3π(-1|((2x - 2)/(-1x - 3)) - 2| - 2) + 3) + 3) - 3)/(-1(3cos(3π(-1|((2x - 2)/(-1x - 3)) - 2| - 2) + 3) + 3) - 1))^2 - 1((3(3cos(3π(-1|((2x - 2)/(-1x - 3)) - 2| - 2) + 3) + 3) - 3)/(-1(3cos(3π(-1|((2x - 2)/(-1x -... | 123 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = (1(-5(-2sin(3π(-1|(-2|x| - 3) + 2| - 2) - 2) - 3) + 1) + 2)/(2(-5(-2sin(3π(-1|(-2|x| - 3) + 2| - 2) - 2) - 3) + 1) - 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 121 | MATH |
[
{
"content": "How many local maxima does the function f(x) = -4(5(-3|(4(-2cos(3πx - 1) - 2) + 1) + 3| - 2) + 4)^2 - 5(5(-3|(4(-2cos(3πx - 1) - 2) + 1) + 3| - 2) + 4) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 52 | MATH |
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