To start the applet right click the slider below and activate the animation. 

t = 5 (slider from -5 to 5, step 0.01)
a: RandomUniform[0, 1] + (0 * t)
b: RandomUniform[0, 8.76] + (0 * t)
F = (0, 0)
g = Circle(F, 25)
c:x^(6) + y^(6) - 1 = 0
f(x) = sin((2 * x))^(2 / 3)
d = Integral(f, 0, b)
A: ((sqrt(a) * cos(d)^(1 / 3)), (sqrt(a) * sin(d)^(1 / 3)))
s = 8.76 (slider from 0 to 10, step 0.01)
e = Integral(f, 0, s)