[User]
How many local extrema (both minima and maxima) does the function f(x) = 1((-3(-1cos(1π(-2|x - 3| - 1) - 2) - 2) + 3)/(-3(-1cos(1π(-2|x - 3| - 1) - 2) - 2)))^2 - 4((-3(-1cos(1π(-2|x - 3| - 1) - 2) - 2) + 3)/(-3(-1cos(1π(-2|x - 3| - 1) - 2) - 2))) + 5 have in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}

dataset: MATH


[User]
Find the x-coordinate of the leftmost local extremum of the function f(x) = 1|(5(-2cos(3π((-1x)/(1x + 2)) - 1) + 3)^2 - 1(-2cos(3π((-1x)/(1x + 2)) - 1) + 3) - 2) - 1| + 1 in the interval [-10, 10]. Round to the nearest integer.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the x-coordinate of the local extremum with the smallest y-value of the function f(x) = (2(5(-2sin(2π(-3|x + 2| - 2)) + 1)^2 + 5(-2sin(2π(-3|x + 2| - 2)) + 1) - 5) + 2)/(-1(5(-2sin(2π(-3|x + 2| - 2)) + 1)^2 + 5(-2sin(2π(-3|x + 2| - 2)) + 1) - 5) - 3) in the interval [-10, 10]. Round to the nearest integer.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many local extrema (both minima and maxima) does the function f(x) = 2|(2cos(1π((3(1x^2 - 4x - 4) - 1)/(-1(1x^2 - 4x - 4) - 1)) + 3) - 1) - 3| - 3 have in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the average of all x-coordinates of local maxima of the function f(x) = 1|(-2((3(2cos(1πx - 1) + 3))/(3(2cos(1πx - 1) + 3) + 3))^2 - 2((3(2cos(1πx - 1) + 3))/(3(2cos(1πx - 1) + 3) + 3)) - 4) + 2| - 1 in the interval [-10, 10]. Round to the nearest integer.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the x-coordinate of the rightmost local maximum of the function f(x) = 1sin(1π((2(-2(1|x + 2| - 3)^2 + 3(1|x + 2| - 3)) + 3)/(1(-2(1|x + 2| - 3)^2 + 3(1|x + 2| - 3))))) + 1 in the interval [-10, 10]. Round to the nearest integer.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = -1|((-3(1(-3sin(3πx))^2 - 3(-3sin(3πx)) - 3) + 1)/(1(1(-3sin(3πx))^2 - 3(-3sin(3πx)) - 3) - 3)) - 1| + 1 in the interval [-10, 10]. Round to the nearest integer.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many local extrema (both minima and maxima) does the function f(x) = 1(2|((1(2cos(1πx - 1) - 3) - 1)/(-2(2cos(1πx - 1) - 3) - 3)) + 3| + 3)^2 - 3(2|((1(2cos(1πx - 1) - 3) - 1)/(-2(2cos(1πx - 1) - 3) - 3)) + 3| + 3) + 2 have in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = (-2(-3(2|(2sin(1πx + 1) - 3)| + 3)^2 + 5(2|(2sin(1πx + 1) - 3)| + 3) + 2) - 1)/(3(-3(2|(2sin(1πx + 1) - 3)| + 3)^2 + 5(2|(2sin(1πx + 1) - 3)| + 3) + 2) + 2) in the interval [-10, 10]. Round to the nearest integer.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the x-coordinate of the leftmost local minimum of the function f(x) = -1sin(2π(-2|((2(-5x^2 - 2x - 1) + 3)/(2(-5x^2 - 2x - 1) - 1)) - 2| + 1) - 2) - 2 in the interval [-10, 10]. Round to the nearest integer.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the x-coordinate of the rightmost local minimum of the function f(x) = -1sin(1π((2(-2|(-3x^2) - 3| - 1))/(1(-2|(-3x^2) - 3| - 1) + 2)) + 1) - 3 in the interval [-10, 10]. Round to the nearest integer.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the average of all x-coordinates of local extrema of the function f(x) = 3cos(2π(1|(-5((1x + 2)/(1x - 2))^2 + 5((1x + 2)/(1x - 2)) + 4) + 1| + 2) + 3) - 2 in the interval [-10, 10]. Round to the nearest integer.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the x-coordinate of the rightmost local minimum of the function f(x) = -3|((-2(-4(-1cos(1πx - 1))^2 + 3(-1cos(1πx - 1)) - 1) - 2)/(-2(-4(-1cos(1πx - 1))^2 + 3(-1cos(1πx - 1)) - 1) - 3)) + 1| + 3 in the interval [-10, 10]. Round to the nearest integer.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -2sin(3π(-5(-1|((-1x - 2)/(1x)) - 1| - 3)^2 - 2) - 3) + 3 in the interval [-10, 10]. Round to the nearest integer.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the x-coordinate of the leftmost local extremum of the function f(x) = 3cos(3π(4((-2(1|x - 3| + 1) + 1)/(1(1|x - 3| + 1) + 2))^2 - 2((-2(1|x - 3| + 1) + 1)/(1(1|x - 3| + 1) + 2)) - 1) - 1) - 3 in the interval [-10, 10]. Round to the nearest integer.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the x-coordinate of the leftmost local maximum of the function f(x) = 3|(-2((2(2cos(3πx + 2)))/(3(2cos(3πx + 2)) + 2))^2 - 4((2(2cos(3πx + 2)))/(3(2cos(3πx + 2)) + 2)) + 1) + 1| + 2 in the interval [-10, 10]. Round to the nearest integer.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 1cos(1π((-3(1(2|x + 2| + 3)^2 - 4(2|x + 2| + 3) - 1) - 3)/(2(1(2|x + 2| + 3)^2 - 4(2|x + 2| + 3) - 1) - 3))) - 2 in the interval [-10, 10]. Round to the nearest integer.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 1sin(3π(1(-3|((1x - 1)/(-3x + 1))| - 3)^2 + 3(-3|((1x - 1)/(-3x + 1))| - 3) + 1) - 3) - 1 in the interval [-10, 10]. Round to the nearest integer.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many local maxima does the function f(x) = 1(-3|((-2(-2cos(3πx + 1) + 2) - 2)/(-3(-2cos(3πx + 1) + 2) + 1))|)^2 + 2(-3|((-2(-2cos(3πx + 1) + 2) - 2)/(-3(-2cos(3πx + 1) + 2) + 1))|) + 1 have in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the x-coordinate of the local minimum with the smallest y-value of the function f(x) = -3sin(2π((3(5(-1|x + 2|)^2 + 5(-1|x + 2|) - 5) - 3)/(3(5(-1|x + 2|)^2 + 5(-1|x + 2|) - 5))) - 3) - 1 in the interval [-10, 10]. Round to the nearest integer.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the x-coordinate of the leftmost local minimum of the function f(x) = -3sin(3π(2|(-5((1x)/(-3x + 2))^2 + 2((1x)/(-3x + 2)) + 2) - 1|) + 3) - 3 in the interval [-10, 10]. Round to the nearest integer.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the x-coordinate of the rightmost local minimum of the function f(x) = -1|(3sin(3π(-5((-2x - 2)/(1x + 2))^2 + 1((-2x - 2)/(1x + 2)) - 1)) + 3) + 3| in the interval [-10, 10]. Round to the nearest integer.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 1cos(3π(2|((-2(-3x^2 - 5x - 5) - 2)/(1(-3x^2 - 5x - 5) + 3)) + 3| + 2)) + 3 in the interval [-10, 10]. Round to the nearest integer.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = 3sin(1π((1(1(-3|x + 1| + 3)^2 + 1(-3|x + 1| + 3) + 5) - 3)/(-2(1(-3|x + 1| + 3)^2 + 1(-3|x + 1| + 3) + 5) + 3)) + 3) + 1 in the interval [-10, 10]. Round to the nearest integer.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the x-coordinate of the leftmost local maximum of the function f(x) = (3(3|(4(-2sin(3πx + 3) + 1)^2 - 5(-2sin(3πx + 3) + 1)) - 3| - 3) - 3)/(-1(3|(4(-2sin(3πx + 3) + 1)^2 - 5(-2sin(3πx + 3) + 1)) - 3| - 3) + 3) in the interval [-10, 10]. Round to the nearest integer.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the x-coordinate of the rightmost local extremum of the function f(x) = (-1(5(2cos(3π(1|x - 3|) - 3))^2 + 4(2cos(3π(1|x - 3|) - 3)) - 3) + 1)/(-3(5(2cos(3π(1|x - 3|) - 3))^2 + 4(2cos(3π(1|x - 3|) - 3)) - 3)) in the interval [-10, 10]. Round to the nearest integer.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the average of all x-coordinates of local maxima of the function f(x) = 3sin(1π((2(-2|(-3x^2 + 4x + 5) - 1| - 2) - 1)/(3(-2|(-3x^2 + 4x + 5) - 1| - 2) - 1)) + 1) + 3 in the interval [-10, 10]. Round to the nearest integer.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the x-coordinate of the local maximum with the smallest y-value of the function f(x) = -1((-3(1sin(1π(1|x + 3| + 2) + 2) - 1))/(-3(1sin(1π(1|x + 3| + 2) + 2) - 1) - 2))^2 + 3((-3(1sin(1π(1|x + 3| + 2) + 2) - 1))/(-3(1sin(1π(1|x + 3| + 2) + 2) - 1) - 2)) - 3 in the interval [-10, 10]. Round to the nearest integer.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = 2cos(1π(-2((1(-1|x - 3| + 1) - 3)/(2(-1|x - 3| + 1) + 2))^2 - 4((1(-1|x - 3| + 1) - 3)/(2(-1|x - 3| + 1) + 2)) + 1) + 1) - 3 in the interval [-10, 10]. Round to the nearest integer.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the x-coordinate of the rightmost local maximum of the function f(x) = 2|((3(4(1cos(1πx + 2) + 1)^2 - 1(1cos(1πx + 2) + 1) + 2) + 2)/(-3(4(1cos(1πx + 2) + 1)^2 - 1(1cos(1πx + 2) + 1) + 2) - 1)) + 2| + 2 in the interval [-10, 10]. Round to the nearest integer.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the x-coordinate of the leftmost local minimum of the function f(x) = -3|(-2((-2(2cos(3πx - 2) + 2) + 1)/(-2(2cos(3πx - 2) + 2) - 2))^2 - 3((-2(2cos(3πx - 2) + 2) + 1)/(-2(2cos(3πx - 2) + 2) - 2)) - 4)| + 3 in the interval [-10, 10]. Round to the nearest integer.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the average of all x-coordinates of local extrema of the function f(x) = (2(-2|(3sin(3π(-1x^2 + 2x + 2) - 2)) + 3| + 2) + 1)/(-2(-2|(3sin(3π(-1x^2 + 2x + 2) - 2)) + 3| + 2) + 3) in the interval [-10, 10]. Round to the nearest integer.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the x-coordinate of the rightmost local maximum of the function f(x) = -2(1sin(2π((-1(-3|x + 2| + 2) + 2)/(3(-3|x + 2| + 2) - 2)) - 3) + 2)^2 - 2(1sin(2π((-1(-3|x + 2| + 2) + 2)/(3(-3|x + 2| + 2) - 2)) - 3) + 2) + 1 in the interval [-10, 10]. Round to the nearest integer.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many local extrema (both minima and maxima) does the function f(x) = 2cos(3π(-1|((-2(2x^2 + 4x + 1) + 3)/(-1(2x^2 + 4x + 1) - 3)) + 1| + 3) + 2) have in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the x-coordinate of the local minimum with the largest y-value of the function f(x) = 4(-3sin(1π((3(-2|x + 1| - 1) + 1)/(-1(-2|x + 1| - 1) + 2)) + 2) + 1)^2 + 1(-3sin(1π((3(-2|x + 1| - 1) + 1)/(-1(-2|x + 1| - 1) + 2)) + 2) + 1) + 4 in the interval [-10, 10]. Round to the nearest integer.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the x-coordinate of the leftmost local minimum of the function f(x) = -1|(-2cos(3π(-1((3x)/(1x + 1))^2 - 1((3x)/(1x + 1)) - 2) + 3) - 3) - 2| - 3 in the interval [-10, 10]. Round to the nearest integer.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the x-coordinate of the rightmost local extremum of the function f(x) = (3(-2sin(3π(-1(-1|x| - 3)^2 + 5(-1|x| - 3) - 3) + 2) - 2) - 3)/(-2(-2sin(3π(-1(-1|x| - 3)^2 + 5(-1|x| - 3) - 3) + 2) - 2) - 1) in the interval [-10, 10]. Round to the nearest integer.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the average of all x-coordinates of local minima of the function f(x) = (1(-1(-1|(-1cos(2πx) - 2)|)^2 - 1(-1|(-1cos(2πx) - 2)|) - 1) - 1)/(-1(-1(-1|(-1cos(2πx) - 2)|)^2 - 1(-1|(-1cos(2πx) - 2)|) - 1) - 3) in the interval [-10, 10]. Round to the nearest integer.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the x-coordinate of the rightmost local minimum of the function f(x) = 2cos(1π(4((-1(-3|x - 1| + 2))/(-3(-3|x - 1| + 2) + 1))^2 + 1((-1(-3|x - 1| + 2))/(-3(-3|x - 1| + 2) + 1)) - 2)) - 2 in the interval [-10, 10]. Round to the nearest integer.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many local extrema (both minima and maxima) does the function f(x) = 5(1|((-3(-3sin(2πx + 2)))/(-3(-3sin(2πx + 2)) + 2)) + 1| - 3)^2 + 3(1|((-3(-3sin(2πx + 2)))/(-3(-3sin(2πx + 2)) + 2)) + 1| - 3) + 1 have in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the x-coordinate of the leftmost local minimum of the function f(x) = -2sin(3π(-4((-1(-2|x - 3| + 2) + 2)/(2(-2|x - 3| + 2) - 3))^2 - 2((-1(-2|x - 3| + 2) + 2)/(2(-2|x - 3| + 2) - 3)) - 2) + 1) - 1 in the interval [-10, 10]. Round to the nearest integer.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many local minima does the function f(x) = 1|(1(-1sin(3π((-3x)/(-2x - 2)) - 2) - 3)^2 + 2(-1sin(3π((-3x)/(-2x - 2)) - 2) - 3) - 5) + 1| have in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the average of all x-coordinates of local maxima of the function f(x) = -3(-2|((-3(3cos(3πx + 2) - 1) + 1)/(-2(3cos(3πx + 2) - 1) + 3)) + 1| + 3)^2 + 5(-2|((-3(3cos(3πx + 2) - 1) + 1)/(-2(3cos(3πx + 2) - 1) + 3)) + 1| + 3) in the interval [-10, 10]. Round to the nearest integer.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the x-coordinate of the local maximum with the largest y-value of the function f(x) = (2(-3|(-2sin(1π(3x^2 - 1x - 2) + 1) - 2) + 3| - 2) + 1)/(3(-3|(-2sin(1π(3x^2 - 1x - 2) + 1) - 2) + 3| - 2) + 1) in the interval [-10, 10]. Round to the nearest integer.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the x-coordinate of the local extremum with the largest y-value of the function f(x) = (-2(-1(-2cos(3π(1|x| + 2) - 2) - 2)^2 - 1(-2cos(3π(1|x| + 2) - 2) - 2) + 2) - 1)/(-2(-1(-2cos(3π(1|x| + 2) - 2) - 2)^2 - 1(-2cos(3π(1|x| + 2) - 2) - 2) + 2)) in the interval [-10, 10]. Round to the nearest integer.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many local extrema (both minima and maxima) does the function f(x) = 1cos(2π(4(-2|((-2x - 2)/(-1x + 2)) + 3| + 1)^2 + 1(-2|((-2x - 2)/(-1x + 2)) + 3| + 1) + 3) - 2) - 2 have in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the x-coordinate of the rightmost local extremum of the function f(x) = (-2(-5(2sin(1π(1|x - 1|) + 1))^2 + 5(2sin(1π(1|x - 1|) + 1)) + 3) - 2)/(-2(-5(2sin(1π(1|x - 1|) + 1))^2 + 5(2sin(1π(1|x - 1|) + 1)) + 3) - 3) in the interval [-10, 10]. Round to the nearest integer.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the x-coordinate of the rightmost local minimum of the function f(x) = -4(1|(1sin(3π((1x + 1)/(1x + 2)) - 1) + 2) - 1| + 3)^2 - 4(1|(1sin(3π((1x + 1)/(1x + 2)) - 1) + 2) - 1| + 3) + 2 in the interval [-10, 10]. Round to the nearest integer.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the average of all x-coordinates of local maxima of the function f(x) = -2((1(2sin(2π(1|x - 1|) - 2) + 2))/(-2(2sin(2π(1|x - 1|) - 2) + 2) - 1))^2 + 3((1(2sin(2π(1|x - 1|) - 2) + 2))/(-2(2sin(2π(1|x - 1|) - 2) + 2) - 1)) - 5 in the interval [-10, 10]. Round to the nearest integer.

Present the answer in LaTex format: \boxed{Your answer}