Let's import NumPy, SciPy, scipy.optimize, and matplotlib:

In [1]: import numpy as np
        import scipy as sp
        import scipy.optimize as opt
        import matplotlib.pyplot as plt
        %matplotlib inline

We define the mathematical function f(x)=cos(x)-x in Python. We will try to find a root of this function numerically. Here, a root corresponds to a fixed point of the cosine function:

In [2]: f = lambda x: np.cos(x) - x

Let's plot this function on the interval [-5, 5] (using 1000 samples):

In [3]: x = np.linspace(-5, 5, 1000)
        y = f(x)
        plt.plot(x, y)
        plt.axhline(0, color='k')
        plt.xlim(-5,5)

We see that this function has a unique root on this interval (this is because the function's sign changes on this interval). The scipy.optimize module contains a few root-finding functions...