http://codeforces.me/gym/100016

I have no idea how to compute integral of f(z)=0.5*(r*r-z*z)*acos(c*z/(r*r-z*z)) (c is a constant and r is the radius of sphere) I can't find its original funtion so I have tried something like simpson, but it is tooooo huge (worst case 2000 times compute) and got tle on test 4... any one have idea how to compute the original funtion thanks....