import math
# ouch, no scipy 

density = lambda t: math.exp(-t*t/2) / math.sqrt(2*math.pi) 
# note acuracy of math.pi 8 digits: maybe better define own

def phi(t):
    tabs = abs(t)
    delta, eps = 0.001, 1e-6
    s = 0
    while ...:
        d = delta * density(tabs)
        s += d
        tabs += delta
        if d < eps: break
    return s if t <= 0 else 1-s

normalize = lambda mu, sigma: lambda t: (t-mu) / sigma

# main

n = normalize(30, 4)

print(phi(n(40)))
print(1-phi(n(21)))
print(phi(n(35)) - phi(n(30)))