from math import *
  
epsilon=10**(-8)
a=0.0
b=1.0
n=8 # Initial number of intervals
M=12  # Max number of times we half h
h=(b-a)/n
I=0
x=a+h/2
for k in range(n):
  I=I+cos(x)
  x=x+h
I=h*I
abserr=abs(I)
print I, sin(1)
j=1
while j<M and abserr>epsilon*abs(I):
  j=j+1
  Ip=I
  n=2*n
  h=(b-a)/n
  I=0
  x=a+h/2
  for k in range(n):
    I=I+cos(x)
    x=x+h
  I=h*I
  print I, sin(1), abs(I-Ip)/abs(Ip)
  abserr=abs(I-Ip)