from numpy import *

def midpointn(f, a, b, n):
    h = (b - a)/n
    return h*sum( f(a+h/2+(arange(n))*h) )
   
def trapezoidaln(f, a, b, n):
    h = (b - a)/n
    return h*( (f(a) + f(b))/2 + sum( f(a+(arange(1,n))*h ) ) )
    
    
def simpsonn(f, a, b, n):
    h = (b - a)/(2*n)
    return h*(f(a) + f(b) + \
           2*sum( f(a+2*h*(arange(1,n))) ) + \
           4*sum( f(a+h+2*h*(arange(n)))))/3
           
midpointn(exp,0,1,10)

print(trapezoidaln(exp,0,1,10))
print(trapezoidaln(lambda x: sin(x)/(1+x**2), 0, pi/2, 6))

print(simpsonn(exp,0,1,10))
print(simpsonn(lambda x: sin(x)/(1+x**2), 0, pi/2, 6))
           
           
def int_vals(n):
    l = (1/n)*sum(exp(arange(n)/n))
    u = (1/n)*sum(exp(arange(1,n+1)/n))
    l_err = abs(l-(exp(1)-1))
    u_err = abs(u-(exp(1)-1))
    return l, u, l_err, u_err

[l, u, l_err, u_err]=int_vals(10)
print(l)
print(u)
print(l_err)
print(u_err)
    
n = 1;
l,u,l_err,u_err=int_vals(n)
while l_err > 3*10**(-3):
    n = n+1
    l,u,l_err,u_err=int_vals(n)
print(n)