messages listlengths 1 1 | ground_truth stringlengths 1 3 | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Determine the total count of local extrema points for the function f(x) = 4((-3(1sin(2π(2|(2|x + 3| + 2) - 1| - 3) - 3) - 3) - 2)/(-2(1sin(2π(2|(2|x + 3| + 2) - 1| - 3) - 3) - 3) + 1))^2 - 5((-3(1sin(2π(2|(2|x + 3| + 2) - 1| - 3) - 3) - 3) - 2)/(-2(1sin(2π(2|(2|x + 3| + 2) - 1| - 3) - 3) - 3) + 1)... | 161 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = -3sin(3π(5((-2(-2|(5x) + 1| - 1) + 2)/(-1(-2|(5x) + 1| - 1) + 2)) + 5) + 2) - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = (-3(-5(3|(-2sin(1π(4x) - 1) + 3) + 1| - 2)^2 - 2(3|(-2sin(1π(4x) - 1) + 3) + 1| - 2) + 4) - 3)/(2(-5(3|(-2sin(1π(4x) - 1) + 3) + 1| - 2)^2 - 2(3|(-2sin(1π(4x) - 1) + 3) + 1| - 2) + 4)) in the interval [-10, 10].\n\nPresent t... | 80 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = 3(5(1(-2(-2sin(3πx + 3) + 2) - 1) + 5)^2 + 2)^2 + 2(5(1(-2(-2sin(3πx + 3) + 2) - 1) + 5)^2 + 2) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 118 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = 2cos(2π((-3(-4(5(-3|x + 3| + 2)^2 - 5(-3|x + 3| + 2) - 2)^2 - 5(5(-3|x + 3| + 2)^2 - 5(-3|x + 3| + 2) - 2)) + 1)/(-2(-4(5(-3|x + 3| + 2)^2 - 5(-3|x + 3| + 2) - 2)^2 - 5(5(-3|x + 3| + 2)^2 - 5(-3|x + 3| + 2) - 2)) - 1)) - 2) ... | 15 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = (-3((2(3sin(3π(-2(-2|x + 1|)^2 - 4(-2|x + 1|) + 2) - 3) - 3) + 1)/(3(3sin(3π(-2(-2|x + 1|)^2 - 4(-2|x + 1|) + 2) - 3) - 3) - 2)) + 3)/(3((2(3sin(3π(-2(-2|x + 1|)^2 - 4(-2|x + 1|) + 2) - 3) - 3) + 1)/(3(3sin(3π(-2(-2|x + 1|)^2 - 4(-2|x + 1... | 481 | MATH |
[
{
"content": "How many local minima does the function f(x) = 2cos(3π(1((2(-2((1x - 3)/(1x)) + 5) - 1)/(-2(-2((1x - 3)/(1x)) + 5) - 1)) - 3) - 1) 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) = 1|(1cos(3π(1(-1|(1|x + 1| - 2) + 3| - 2) - 3) + 3) + 2) + 3| + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 31 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = -5(1sin(2π(2|(-1((-1x - 1)/(1x - 2)) + 5) - 3| - 1) - 1) + 3)^2 - 4(1sin(2π(2|(-1((-1x - 1)/(1x - 2)) + 5) - 3| - 1) - 1) + 3) + 5 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 31 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = (1(3(-4((2(-2sin(3πx) + 1))/(1(-2sin(3πx) + 1) - 3))^2 - 4((2(-2sin(3πx) + 1))/(1(-2sin(3πx) + 1) - 3)) - 3)^2 - 5(-4((2(-2sin(3πx) + 1))/(1(-2sin(3πx) + 1) - 3))^2 - 4((2(-2sin(3πx) + 1))/(1(-2sin(3πx) + 1) - 3)) - 3)) +... | 120 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1(-2(3|(-3sin(2π((-1x - 2)/(3x + 2)) + 3) - 3)| - 2)^2 + 2(3|(-3sin(2π((-1x - 2)/(3x + 2)) + 3) - 3)| - 2)) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 24 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = (1(-5(-1cos(1π(-1(1x^2 + 5x + 3) - 4) + 1) - 1)^2 - 4(-1cos(1π(-1(1x^2 + 5x + 3) - 4) + 1) - 1) + 4) + 2)/(3(-5(-1cos(1π(-1(1x^2 + 5x + 3) - 4) + 1) - 1)^2 - 4(-1cos(1π(-1(1x^2 + 5x + 3) - 4) + 1) - 1) + 4) - 1) in the interval [-10, 10].... | 189 | MATH |
[
{
"content": "How many local maxima does the function f(x) = -1|(1(5(3cos(3π((2x)/(-3x + 1)) + 2) + 2)^2 - 2(3cos(3π((2x)/(-3x + 1)) + 2) + 2))^2 - 4(5(3cos(3π((2x)/(-3x + 1)) + 2) + 2)^2 - 2(3cos(3π((2x)/(-3x + 1)) + 2) + 2)) + 5) - 1| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: ... | 11 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = (-1(3(3(1(5x^2 - 5x - 4)^2 - 2(5x^2 - 5x - 4) - 3)^2 + 2(1(5x^2 - 5x - 4)^2 - 2(5x^2 - 5x - 4) - 3) - 5)^2 - 2(3(1(5x^2 - 5x - 4)^2 - 2(5x^2 - 5x - 4) - 3)^2 + 2(1(5x^2 - 5x - 4)^2 - 2(5x^2 - 5x - 4) - 3) - 5) - 4) + 3)/(1(3(3(1(5x^2 - 5x... | 15 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1|(-4(1|(1(4x^2 + 3x - 5) + 4) - 2| - 3) + 5) - 3| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = -3(-1|(1sin(1π(5(-2x^2 - 3x + 2) - 4)) + 2) - 3| - 1) + 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 250 | MATH |
[
{
"content": "How many local maxima does the function f(x) = 5(-3sin(3π(4((2(-1x^2 + 4x + 5) + 2)/(-2(-1x^2 + 4x + 5) - 3))^2 + 5((2(-1x^2 + 4x + 5) + 2)/(-2(-1x^2 + 4x + 5) - 3)) - 2) + 3) - 1)^2 + 4(-3sin(3π(4((2(-1x^2 + 4x + 5) + 2)/(-2(-1x^2 + 4x + 5) - 3))^2 + 5((2(-1x^2 + 4x + 5) + 2)/(-2(-1x^2 + 4x + 5) ... | 20 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = (1(1(2((1(2x + 2) - 2)/(-3(2x + 2) - 1))^2 - 4((1(2x + 2) - 2)/(-3(2x + 2) - 1)) - 4)^2 + 2(2((1(2x + 2) - 2)/(-3(2x + 2) - 1))^2 - 4((1(2x + 2) - 2)/(-3(2x + 2) - 1)) - 4) - 4) + 2)/(2(1(2((1(2x + 2) - 2)/(-3(2x + 2) - 1... | 4 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = -1(1|(1(1sin(1π(-3x^2 - 2x - 3) - 2) - 3)^2 + 2(1sin(1π(-3x^2 - 2x - 3) - 2) - 3) + 4) + 3| - 2) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 334 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = -1|(-3|(-3(-2e^(-1(1x^2 - 4x + 3)) - 1) - 4) + 2| + 3) - 1| + 2 where -10 ≤ x ≤ 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) = (-1(2cos(2π(3|((3(-4x - 2) - 3)/(-2(-4x - 2) + 3)) + 2|) + 1) + 2))/(3(2cos(2π(3|((3(-4x - 2) - 3)/(-2(-4x - 2) + 3)) + 2|) + 1) + 2)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 57 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = -3|(-3|(-4(1|(2x^2 - 5x - 3) - 1| - 1) + 2) - 1|) - 2| - 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = 4(2(1|((3(2sin(1πx + 3) - 1) + 2)/(3(2sin(1πx + 3) - 1) + 1)) - 2| + 2)^2 + 3(1|((3(2sin(1πx + 3) - 1) + 2)/(3(2sin(1πx + 3) - 1) + 1)) - 2| + 2) - 5)^2 - 4(2(1|((3(2sin(1πx + 3) - 1) + 2)/(3(2sin(1πx + 3) - 1) + 1)) - 2| + 2)^2 + 3(1|((3... | 40 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = -1|((-1(-1(-3|((3x + 2)/(2x + 3))| - 2)^2 - 5(-3|((3x + 2)/(2x + 3))| - 2) - 5) + 3)/(-3(-1(-3|((3x + 2)/(2x + 3))| - 2)^2 - 5(-3|((3x + 2)/(2x + 3))| - 2) - 5) - 1)) + 1| have in the interval [-10, 10]?\n\nPresent the an... | 8 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = 2cos(3π((-3(-1(1(3x^2 - 4) - 5) + 3))/(-1(-1(1(3x^2 - 4) - 5) + 3) + 2)) - 1) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 26 | MATH |
[
{
"content": "How many local minima does the function f(x) = -3|(-1(1(-1cos(2π(-1x + 2) - 3) + 2)^2 - 5(-1cos(2π(-1x + 2) - 3) + 2) + 1) - 2) - 3| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 100 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = -2(1e^(-1((3(4(-2|x + 2| + 3)^2 - 2(-2|x + 2| + 3) - 4) + 3)/(1(4(-2|x + 2| + 3)^2 - 2(-2|x + 2| + 3) - 4) - 2))) + 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 6 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = -3(4((-1((3(3cos(1πx - 3) + 2) - 3)/(-2(3cos(1πx - 3) + 2) - 3)) + 3)/(3((3(3cos(1πx - 3) + 2) - 3)/(-2(3cos(1πx - 3) + 2) - 3)) - 2))^2 - 5) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\bo... | 60 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = 1|(3((-1(1sin(1π((2x - 3)/(-3x - 1)) - 3) - 2) + 1)/(2(1sin(1π((2x - 3)/(-3x - 1)) - 3) - 2) + 1)))| + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6 | MATH |
[
{
"content": "How many local maxima does the function f(x) = 4(3(1sin(1π(-3|(3|x - 1| - 1) - 3| - 1) + 3)) + 4)^2 + 5(3(1sin(1π(-3|(3|x - 1| - 1) - 3| - 1) + 3)) + 4) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 90 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = 2|(2|((-2(1cos(1π(1x^2 + 4) - 3) - 2) + 3)/(1(1cos(1π(1x^2 + 4) - 3) - 2) - 3)) + 3| - 1)| + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 101 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = -2(-5(-2((2(-4x^2 - 1x + 5) + 1)/(1(-4x^2 - 1x + 5) - 3))^2 + 1((2(-4x^2 - 1x + 5) + 1)/(1(-4x^2 - 1x + 5) - 3)) + 4) - 5) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 5 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = (3(2|(1cos(1π(-2(-3x - 1) - 3) + 3) + 3) + 3| - 2) + 2)/(2(2|(1cos(1π(-2(-3x - 1) - 3) + 3) + 3) + 3| - 2) + 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = -2(3|(1sin(3π(1(1|x - 1| + 1)^2 + 2(1|x - 1| + 1) + 4) - 3)) - 1| + 2)^2 + 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 271 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = -1|(1sin(1π(2((-3(3x^2 + 5x - 3) - 2)/(2(3x^2 + 5x - 3)))^2 + 3((-3(3x^2 + 5x - 3) - 2)/(2(3x^2 + 5x - 3))) + 3) - 1) - 1)| in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = 3(-4(-2|(-2(-2x^2 + 2)^2 - 2(-2x^2 + 2) - 3) + 3| - 1) + 3)^2 + 3(-4(-2|(-2(-2x^2 + 2)^2 - 2(-2x^2 + 2) - 3) + 3| - 1) + 3) - 5 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = 2sin(3π(-3|(-2(-2|(3x^2 + 4x + 3) - 3| - 1)^2 - 1(-2|(3x^2 + 4x + 3) - 3| - 1) - 4) + 2|)) - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 102 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = 4(2cos(3π(-4(-3|(-1|x + 1| + 2) + 1| + 3)^2 - 2) + 2) - 3)^2 - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 432 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = 1sin(1π((-1(2|(4((-1x)/(1x - 3)) - 3)| - 1))/(3(2|(4((-1x)/(1x - 3)) - 3)| - 1) - 2)) + 1) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = -3(1sin(3π(5((3(2|x| - 3) + 2)/(3(2|x| - 3) - 1))^2 - 4) - 1) - 1)^2 + 5(1sin(3π(5((3(2|x| - 3) + 2)/(3(2|x| - 3) - 1))^2 - 4) - 1) - 1) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 50 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = 2((-3(3sin(3π(4(-3|x + 1| + 1)^2 + 2) - 2) + 1) - 3)/(-1(3sin(3π(4(-3|x + 1| + 1)^2 + 2) - 2) + 1)))^2 + 3((-3(3sin(3π(4(-3|x + 1| + 1)^2 + 2) - 2) + 1) - 3)/(-1(3sin(3π(4(-3|x + 1| + 1)^2 + 2) - 2) + 1))) + 1 in the interval [-10, 10].\n... | 211 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = 1(1sin(1π(3(-1|(5x + 3) + 2| + 3) + 5) + 3) - 2) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 301 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = -4(4(-3(-2cos(3π(1x^2 - 4x - 1) + 1) - 1)^2 + 5(-2cos(3π(1x^2 - 4x - 1) + 1) - 1) - 1) + 3)^2 + 3(4(-3(-2cos(3π(1x^2 - 4x - 1) + 1) - 1)^2 + 5(-2cos(3π(1x^2 - 4x - 1) + 1) - 1) - 1) + 3) + 5 in the interval [-10, 10].\n\nPre... | 315 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = (1(2|(4(-3sin(1π(3|x - 3| - 3) + 2) + 3) - 1) + 2| + 3))/(1(2|(4(-3sin(1π(3|x - 3| - 3) + 2) + 3) - 1) + 2| + 3) + 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 61 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = 1sin(3π(1|((1(2(3|x| + 1) - 3) + 1)/(-2(2(3|x| + 1) - 3) - 1)) + 1| - 2) - 1) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "How many local maxima does the function f(x) = 3sin(2π((2((-2(-2|((-3x - 3)/(1x + 2)) - 2| + 3) - 3)/(1(-2|((-3x - 3)/(1x + 2)) - 2| + 3) - 2)))/(2((-2(-2|((-3x - 3)/(1x + 2)) - 2| + 3) - 3)/(1(-2|((-3x - 3)/(1x + 2)) - 2| + 3) - 2)) - 1)) - 1) - 1 have in the interval [-10, 10]?\n\nPresent the an... | 4 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = (-3(5(-3(-2(-2cos(3πx) - 1)^2 - 4(-2cos(3πx) - 1)) + 2)^2 - 1(-3(-2(-2cos(3πx) - 1)^2 - 4(-2cos(3πx) - 1)) + 2) - 3) + 2)/(-1(5(-3(-2(-2cos(3πx) - 1)^2 - 4(-2cos(3πx) - 1)) + 2)^2 - 1(-3(-2(-2cos(3πx) - 1)^2 - 4(-2cos(3πx) - 1)) + 2) - 3)... | 161 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = (-1(-2|(-5((-2(-3sin(2πx + 2) - 3) - 2)/(1(-3sin(2πx + 2) - 3) - 2))^2 - 1((-2(-3sin(2πx + 2) - 3) - 2)/(1(-3sin(2πx + 2) - 3) - 2)) + 1)| + 3) - 1)/(-1(-2|(-5((-2(-3sin(2πx + 2) - 3) - 2)/(1(-3sin(2πx + 2) - 3) - 2))^2 - 1((-2(-3sin(2πx ... | 80 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = (-1((2(1cos(3π(1(2x^2 - 1x - 3) + 5) + 3) - 1) - 3)/(2(1cos(3π(1(2x^2 - 1x - 3) + 5) + 3) - 1) - 1)) + 1)/(-2((2(1cos(3π(1(2x^2 - 1x - 3) + 5) + 3) - 1) - 3)/(2(1cos(3π(1(2x^2 - 1x - 3) + 5) + 3) - 1) - 1)) - 2) where -10 ≤ x ≤ 10.\n\nPre... | 451 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = 3(3|(-2(3|(3cos(3πx + 3) + 2) + 2| + 3)^2 + 5(3|(3cos(3πx + 3) + 2) + 2| + 3) + 4) - 3| - 3)^2 + 2(3|(-2(3|(3cos(3πx + 3) + 2) + 2| + 3)^2 + 5(3|(3cos(3πx + 3) + 2) + 2| + 3) + 4) - 3| - 3) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex fo... | 26 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = -3e^(2(-2((3(-3(1|x - 1| - 2)) + 1)/(-2(-3(1|x - 1| - 2)) + 3))^2 + 4((3(-3(1|x - 1| - 2)) + 1)/(-2(-3(1|x - 1| - 2)) + 3)) + 2)) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "How many local maxima does the function f(x) = (-3(-4(-2sin(1π(-5(-2x - 4) + 5) - 2) - 3) + 4))/(1(-4(-2sin(1π(-5(-2x - 4) + 5) - 2) - 3) + 4) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 100 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = (-2(2|(2(-2sin(3π(1x^2 - 5x - 2) - 3) + 2) - 2) - 1| + 2))/(-2(2|(2(-2sin(3π(1x^2 - 5x - 2) - 3) + 2) - 2) - 1| + 2) + 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 516 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = 2|(-1|(5(-2(-3sin(2πx - 2) + 1)^2 + 4(-3sin(2πx - 2) + 1) + 1) + 3)| + 3) + 2| + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 179 | MATH |
[
{
"content": "How many local minima does the function f(x) = -1(-3(-3(-2|(1x^2 - 4x + 3) - 1| + 1)^2 + 5(-2|(1x^2 - 4x + 3) - 1| + 1) + 1)^2 - 3(-3(-2|(1x^2 - 4x + 3) - 1| + 1)^2 + 5(-2|(1x^2 - 4x + 3) - 1| + 1) + 1) - 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your an... | 4 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = -5(-4((1(2|(-2sin(2πx - 1) - 2) - 2|) + 1)/(-2(2|(-2sin(2πx - 1) - 2) - 2|)))^2 - 3((1(2|(-2sin(2πx - 1) - 2) - 2|) + 1)/(-2(2|(-2sin(2πx - 1) - 2) - 2|))) - 1) + 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed... | 20 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = 3|(2cos(2π(1|((-2(2|x - 2| - 1) + 2)/(1(2|x - 2| - 1) - 3)) - 2| + 2) + 3) - 1)| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 107 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = 5(-4((-1((2(-3|x| + 2))/(-1(-3|x| + 2) - 3)) - 3)/(3((2(-3|x| + 2))/(-1(-3|x| + 2) - 3)) + 2))^2 - 5((-1((2(-3|x| + 2))/(-1(-3|x| + 2) - 3)) - 3)/(3((2(-3|x| + 2))/(-1(-3|x| + 2) - 3)) + 2)))^2 - 4(-4((-1((2(-3|x| + 2))/(-1(... | 9 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = (-2(-3(1|(-2|(-1sin(3πx))| + 2) - 2| + 2) + 3))/(-1(-3(1|(-2|(-1sin(3πx))| + 2) - 2| + 2) + 3) - 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 119 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = -1(-3sin(2π((3((3(1|x + 1| - 2))/(1(1|x + 1| - 2) + 2)) + 3)/(-2((3(1|x + 1| - 2))/(1(1|x + 1| - 2) + 2)) + 1)) + 3) + 1)^2 + 2(-3sin(2π((3((3(1|x + 1| - 2))/(1(1|x + 1| - 2) + 2)) + 3)/(-2((3(1|x + 1| - 2))/(1(1|x + 1| - 2) + 2)) + 1)) +... | 114 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = (3(-2(3e^(-2(-4(-1x) + 2)) + 3) - 2) + 2)/(1(-2(3e^(-2(-4(-1x) + 2)) + 3) - 2) + 2) 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) = -1cos(3π(5(3|(-2|((2x + 3)/(-2x - 2)) - 2| - 1) + 2| + 3) + 1) + 2) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 68 | MATH |
[
{
"content": "How many local maxima does the function f(x) = 3|((2(-1(1(-2cos(2πx - 3) + 2) - 4)^2 - 5(1(-2cos(2πx - 3) + 2) - 4) + 1) - 1)/(2(-1(1(-2cos(2πx - 3) + 2) - 4)^2 - 5(1(-2cos(2πx - 3) + 2) - 4) + 1) + 2)) + 2| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer... | 40 | MATH |
[
{
"content": "How many local minima does the function f(x) = (2(-4(-3sin(3π(5(4x^2 - 2x + 3)^2 + 2(4x^2 - 2x + 3) - 5) - 1) + 3) + 1) - 2)/(-2(-4(-3sin(3π(5(4x^2 - 2x + 3)^2 + 2(4x^2 - 2x + 3) - 5) - 1) + 3) + 1) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 17 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = (-2((-2(-5(-2sin(1π(-1|x - 2| + 2) + 1) + 1)^2 + 4(-2sin(1π(-1|x - 2| + 2) + 1) + 1) + 5))/(-1(-5(-2sin(1π(-1|x - 2| + 2) + 1) + 1)^2 + 4(-2sin(1π(-1|x - 2| + 2) + 1) + 1) + 5) + 2)) + 2)/(2((-2(-5(-2sin(1π(-1|x - 2| + 2) + 1) + 1)^2 + 4(... | 20 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = -3|(5(1cos(3π(-4(-4x + 1) + 2) - 3) - 1)^2 + 5(1cos(3π(-4(-4x + 1) + 2) - 3) - 1) - 3) + 3| + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 648 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = -5(-2(1cos(3π((-2(4x^2 - 3x) - 1)/(3(4x^2 - 3x) - 2)) + 2) - 3) + 3) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 26 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = -2|((-1(-1(-2(-3sin(3πx - 1) + 3) + 2) + 2) + 3)/(-3(-1(-2(-3sin(3πx - 1) + 3) + 2) + 2) - 3)) - 3| + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "How many local extrema (minima and maxima combined) does the function f(x) = (-2(2(3sin(1π(5(1x^2 + 3x - 5)^2 - 1(1x^2 + 3x - 5) - 1) - 3))^2 + 3(3sin(1π(5(1x^2 + 3x - 5)^2 - 1(1x^2 + 3x - 5) - 1) - 3)) + 3) - 3)/(-2(2(3sin(1π(5(1x^2 + 3x - 5)^2 - 1(1x^2 + 3x - 5) - 1) - 3))^2 + 3(3sin(1π(5(1x^2 +... | 294 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = -4(2(-3sin(1π(4(-1x + 4)^2 - 1(-1x + 4) - 4) - 2) + 2) - 3)^2 - 4 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 439 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = (-3(-1(-2(-3(-2sin(2πx + 2)))^2 - 3(-3(-2sin(2πx + 2))) - 1)^2 + 2(-2(-3(-2sin(2πx + 2)))^2 - 3(-3(-2sin(2πx + 2))) - 1) - 3) + 1)/(1(-1(-2(-3(-2sin(2πx + 2)))^2 - 3(-3(-2sin(2πx + 2))) - 1)^2 + 2(-2(-3(-2sin(2πx + 2)))^2 - ... | 80 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = -5(2|((1(-1sin(1π(-2x^2 + 4x + 1) - 2) - 2) - 1)/(3(-1sin(1π(-2x^2 + 4x + 1) - 2) - 2) + 2)) + 1| + 1) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 299 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = 5(4(-2cos(3π(5(1x^2 + 5x + 2)) + 1) + 2)^2 - 2) + 4 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 485 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = 2sin(1π(-2|(2|(3(1x + 3) - 1) + 1| - 1) + 3| - 3) - 3) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 241 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = -4((2(3cos(1π(-1((-3x - 2)/(-2x + 3))^2 - 4((-3x - 2)/(-2x + 3)) + 2) - 1) + 3))/(2(3cos(1π(-1((-3x - 2)/(-2x + 3))^2 - 4((-3x - 2)/(-2x + 3)) + 2) - 1) + 3) - 1)) + 5 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}... | 56 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = -4((3(-1cos(3π((2(-5x - 1) - 1)/(-2(-5x - 1) + 3)) - 3) - 2) + 2)/(2(-1cos(3π((2(-5x - 1) - 1)/(-2(-5x - 1) + 3)) - 3) - 2) - 3))^2 + 5((3(-1cos(3π((2(-5x - 1) - 1)/(-2(-5x - 1) + 3)) - 3) - 2) + 2)/(2(-1cos(3π((2(-5x - 1) - 1)/(-2(-5x - 1) + 3)) ... | 9 | MATH |
[
{
"content": "How many local maxima does the function f(x) = 1|(2|(2sin(2π(-3|(3|x + 2| - 2)| - 3) - 2) + 3) + 2| + 3) + 1| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 180 | MATH |
[
{
"content": "How many local maxima does the function f(x) = 4((-2(1|(-5(3cos(2πx + 1)) + 4) - 1| + 3))/(-2(1|(-5(3cos(2πx + 1)) + 4) - 1| + 3) - 2)) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 79 | MATH |
[
{
"content": "Find the number of local maximum points for f(x) = -2(1|(-3(5(1sin(1πx + 3) + 3)^2 - 5(1sin(1πx + 3) + 3) + 2)^2 + 5(5(1sin(1πx + 3) + 3)^2 - 5(1sin(1πx + 3) + 3) + 2) - 3) - 3| - 3) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "Find the total number of local minima and maxima for f(x) = -2(-5(2(2sin(2π(-2|x - 1|))) + 1)^2 - 5(2(2sin(2π(-2|x - 1|))) + 1) + 3) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 161 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = -1sin(2π(-4(4(1(-1x^2 - 3x - 4) + 3)^2 - 1(1(-1x^2 - 3x - 4) + 3) - 3) - 5)) + 2 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 124 | MATH |
[
{
"content": "How many local minima does the function f(x) = 5(3sin(2π(4(2|(2|x - 3| + 1)| - 2) + 1) + 1) - 3)^2 - 3(3sin(2π(4(2|(2|x - 3| + 1)| - 2) + 1) + 1) - 3) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 357 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = (-3(-4(2|(-4(-3sin(2πx) - 1) + 2) - 2| - 3)^2 + 1(2|(-4(-3sin(2πx) - 1) + 2) - 2| - 3) + 1) + 1)/(1(-4(2|(-4(-3sin(2πx) - 1) + 2) - 2| - 3)^2 + 1(2|(-4(-3sin(2πx) - 1) + 2) - 2| - 3) + 1) - 3) in the interval [-10, 10].\n\nP... | 160 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = 1|(-5(1sin(3π(1(-3|x - 2| - 1) - 4) + 2) - 1)^2 + 3(1sin(3π(1(-3|x - 2| - 1) - 4) + 2) - 1)) - 3| + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 90 | MATH |
[
{
"content": "How many local minima does the function f(x) = -2(2|(2|(3cos(3π(-4x - 3) + 1) - 3) + 3| - 2) - 2| + 3) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 913 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = -1((2(-3|(-3|(-2sin(3πx + 2) - 2) + 1| + 1) + 2| - 1) - 1)/(1(-3|(-3|(-2sin(3πx + 2) - 2) + 1| + 1) + 2| - 1) + 2)) + 4 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 186 | MATH |
[
{
"content": "How many local minima does the function f(x) = (1(5(1cos(3π(-2|(5x^2 + 1x - 5) + 3| - 2) - 2) - 2)^2 + 3(1cos(3π(-2|(5x^2 + 1x - 5) + 3| - 2) - 2) - 2) - 5) - 2)/(-3(5(1cos(3π(-2|(5x^2 + 1x - 5) + 3| - 2) - 2) - 2)^2 + 3(1cos(3π(-2|(5x^2 + 1x - 5) + 3| - 2) - 2) - 2) - 5) - 2) have in the interval... | 319 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = -1((-3(2(-3sin(1π(-3x^2 + 1x + 5) + 3) - 2)^2 + 4(-3sin(1π(-3x^2 + 1x + 5) + 3) - 2) + 1) - 3)/(-1(2(-3sin(1π(-3x^2 + 1x + 5) + 3) - 2)^2 + 4(-3sin(1π(-3x^2 + 1x + 5) + 3) - 2) + 1) - 2)) + 4 in the interval [-10, 10].\n\nPr... | 471 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = (-3(1e^(-1(2|(-1((2x - 3)/(-2x - 3))^2 + 1((2x - 3)/(-2x - 3)))|)) + 1) + 2)/(2(1e^(-1(2|(-1((2x - 3)/(-2x - 3))^2 + 1((2x - 3)/(-2x - 3)))|)) + 1) - 3) in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\box... | 4 | MATH |
[
{
"content": "How many local minima does the function f(x) = 1(3((2(-1cos(1π((2x + 3)/(-1x - 2))) + 2) + 3)/(-1(-1cos(1π((2x + 3)/(-1x - 2))) + 2) - 3))^2 - 3((2(-1cos(1π((2x + 3)/(-1x - 2))) + 2) + 3)/(-1(-1cos(1π((2x + 3)/(-1x - 2))) + 2) - 3)) + 2)^2 - 2(3((2(-1cos(1π((2x + 3)/(-1x - 2))) + 2) + 3)/(-1(-1cos... | 9 | MATH |
[
{
"content": "How many local maxima does the function f(x) = (2((3((3(-2cos(1π(-1x - 2) + 3) - 2) + 1)/(-1(-2cos(1π(-1x - 2) + 3) - 2) - 2)) - 3)/(-3((3(-2cos(1π(-1x - 2) + 3) - 2) + 1)/(-1(-2cos(1π(-1x - 2) + 3) - 2) - 2)) - 3)) + 2)/(-2((3((3(-2cos(1π(-1x - 2) + 3) - 2) + 1)/(-1(-2cos(1π(-1x - 2) + 3) - 2) - ... | 10 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = 1(-3|((-1(3|(2x - 3) - 1| - 1) + 3)/(1(3|(2x - 3) - 1| - 1) - 2)) - 1| + 3)^2 + 2(-3|((-1(3|(2x - 3) - 1| - 1) + 3)/(1(3|(2x - 3) - 1| - 1) - 2)) - 1| + 3) + 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format... | 8 | MATH |
[
{
"content": "Determine the total count of local extrema points for the function f(x) = 1|(-4(-2(-1(2|x - 1|)^2 - 5(2|x - 1|) + 5)^2 + 1(-1(2|x - 1|)^2 - 5(2|x - 1|) + 5) + 4)^2) - 3| - 1 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "Determine the count of local maxima for the function f(x) = 4(-1(1(-2|(-1x^2 + 2x + 1)| + 2) + 1)^2 + 2(1(-2|(-1x^2 + 2x + 1)| + 2) + 1) - 3) - 3 in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = 3(-2|(-2|(-3(3sin(2πx - 2) - 2)^2 + 2(3sin(2πx - 2) - 2) - 5)|) - 3| + 2)^2 + 3(-2|(-2|(-3(3sin(2πx - 2) - 2)^2 + 2(3sin(2πx - 2) - 2) - 5)|) - 3| + 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 40 | MATH |
[
{
"content": "How many local maxima does the function f(x) = -3(2sin(2π(-2(5(4x^2 - 3x - 4)^2 + 1(4x^2 - 3x - 4) - 1) - 2)) + 2) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 62 | MATH |
[
{
"content": "Determine the count of local minima for the function f(x) = 3((2(-2|(-1|(3sin(3πx - 1) + 1) - 2| + 1) - 1| + 1) + 1)/(2(-2|(-1|(3sin(3πx - 1) + 1) - 2| + 1) - 1| + 1) + 2))^2 - 1((2(-2|(-1|(3sin(3πx - 1) + 1) - 2| + 1) - 1| + 1) + 1)/(2(-2|(-1|(3sin(3πx - 1) + 1) - 2| + 1) - 1| + 1) + 2)) in the i... | 189 | MATH |
[
{
"content": "Find the number of local minimum points for f(x) = -3|(2(-3(-3|(-1sin(1πx - 1) - 3) - 1| + 3)^2 - 1) + 3) - 2| where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "How many local maxima does the function f(x) = (-1(2|(-1cos(1π(3(-2x + 1) + 1) + 2) + 2)| + 3) - 1)/(-3(2|(-1cos(1π(3(-2x + 1) + 1) + 2) + 2)| + 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 maxima does the function f(x) = 1sin(2π(-2(-5(-2((2x)/(2x - 3))^2 - 4((2x)/(2x - 3)) - 3) + 2)) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 142 | MATH |
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