N=np.zeros(31)
for n in range(1,32):
        N[n-1]=(2**n)
def sin(x):
    return np.sin(x)

def midpoint(f,a,b,N):
    h=(b-a)/N

    mysum=0
    for i in np.arange(N):
        mysum+=f(a+i*h+.5*h)*h
    return mysum
print(midpoint(sin,0,np.pi / 2,10000))

def leftpoint(f,a,b,N):
    h=(b-a)/N

    mysum2=0
    for i in np.arange(N):
        mysum2+=f(a+i*h)*h

    return mysum2
print(leftpoint(sin,0,np.pi/2,10000))
x=N
y=abs(1-midpoint(sin,0,np.pi/2,10000))
plt.loglog(x,y)
#this is just for midpoint  so far because i redid it.