Question: How do you make a higher order function in Python?

You have two choices: you can use nested scopes or you can use callable objects.

For example, 
suppose you wanted to define linear(a,b) which returns a function f(x) that computes the value a*x+b. Using nested scopes:

def linear(a,b): 
  def result(x):
    return a*x + b
      return result

Or using a callable object: 

class linear: 
  def __init__(self, a, b):
    self.a, self.b = a,b
    def __call__(self, x):
      return self.a * x + self.b

In both cases: 
taxes = linear(0.3,2)
gives a callable object where taxes(10e6) == 0.3 * 10e6 + 2.

 
The callable object approach has the disadvantage that it is a bit slower and results in slightly longer code. However, note that a collection of callables can share their signature via inheritance:

class exponential(linear): 
  # __init__ inherited
  def __call__(self, x):
    return self.a * (x ** self.b)

Object can encapsulate state for several methods: 
class counter:
  value = 0
    def set(self, x): self.value = x
    def up(self): self.value=self.value+1
    def down(self): self.value=self.value-1
    count = counter()
    inc, dec, reset = count.up, count.down, count.set

Here inc(), dec() and reset() act like functions which share the same counting variable.