from math import *

def sqr(a):
        return sqrt(1.0 - a**2)

def trapez(f, a, b, n):
        h = (b-a) / n
        sum = f(a)
        for i in range (1,n):
                sum = sum + 2 * f(a + h * i)
        sum = sum + f(b)
        return 0.5 * h * sum

print( 4*trapez(sqr,0.,1.,100))
print( 4*trapez(sqr,0.,1.,1000))
print( 4*trapez(sqr,0,1,100))   # Why the error ?