def sum_naturals(n):
    """Sum the first N natural numbers.

    >>> sum_naturals(5)
    15
    """
    total, k = 0, 1
    while k <= n:
        total, k = total + k, k + 1
    return total

def sum_cubes(n):
    """Sum the first N cubes of natural numbers.

    >>> sum_cubes(5)
    225
    """
    total, k = 0, 1
    while k <= n:
        total, k = total + pow(k, 3), k + 1
    return total

identity = lambda k: k
cube = lambda k: pow(k, 3)

def summation(n, term):
    """Sum the first N terms of a sequence.

    >>> summation(5, cube)
    225
    """
    total, k = 0, 1
    while k <= n:
        total, k = total + term(k), k + 1
    return total

def sum_naturals(n):
    return summation(n, identity)

def sum_cubes(n):
    return summation(n, cube)

f = lambda k: 8 / (4 * k - 1) / (4 * k - 3)
summation(1000000, f)

def make_adder(n):
    """Return a function that takes one
    argument K and returns K + N.

    >>> add_three = make_adder(3)
    >>> add_three(4)
    7
    """
    def adder(k):
        return k + n
    return adder

def square(x):
    return x * x

def triple(x):
    return 3 * x

def compose1(f, g):
    """Return a function that composes f and g.

    f, g -- functions of a single argument
    """
    def h(x):
        return f(g(x))
    return h

squiple = compose1(square, triple)
tripare = compose1(triple, square)
squadder = compose1(square, make_adder(2))

squiple(5)  # 225
tripare(5)  # 75
squadder(5) # 49

(lambda x, y: x * y + 1)(3, 4)
(lambda x: lambda y: x * y + 1)(3)(4)