from math import *

def y(x):
	return sqrt(1.0 - x**2)

def trapez(f, a, b, n):
	h = (b-a) / n
	sum = 0
	x = 0.5 * h   # f(x) at middle of the slice
	for i in range (1,n):
		sum = sum + h * f(x)
		x = x + h
	return sum

print 4 * trapez(y, 0., 1.0,1000)
print 4 * trapez(y, 0., 1.,10000)
print 4 * trapez(y, 0, 2, 1000)   # Why the error ?