from math import exp

a=0
b=1

#a
n=10
h=float(b-a)/n
I=0
x=a+h/2
for k in range(n):
    I=I+exp(x)
    x=x+h
print h*I

#b
N=60
eps=10**(-10)
n=1
    
h=float(b-a)/n
I=0
x=a+h/2
for k in range(n):
    I=I+exp(x)
    x=x+h
I=I*h
    
i=1
print 'h: ', h, 'Estimate: ', I
print '  Exact absolute error: ', abs(I-(exp(1)-1))
abserr=abs(I)
while i<N and abserr>eps*I:
    i=i+1
    Ip=I
    n=n*2
        
    h=float(b-a)/n
    I=0
    x=a+h/2
    for k in range(n):
        I=I+exp(x)
        x=x+h
    I=I*h
    
    abserr=abs(I-Ip)
    print 'h: ', h, 'Estimate: ', I
    print '  Estimated absolute error: ', abserr
    print '  Exact absolute error: ', abs(I-(exp(1)-1))
print I