How to perform function approximation in python?

Question

Mathematics

I'm new to python

• The following function is given on the interval x ∈ [-π, π]:
  V(x)=0.8(x²-π²)+1.3cos(7x/2)
  Approximate this function by a piecewise constant function , assuming that V(x) is known with a relative accuracy of 0.83% in the space norm ([-π, π])
  
  

The program, when launched and the user enters a number , as a result of the work should output:

1. Graph of the function V(x)
   
2. Function graph (on the same scale as the V(x) graph)
   
3. The number m is the number of intervals on each of which the function is constant