crude_monte_carlo.py

def crude_monte_carlo(num_samples=5000):
    """
    This function performs the Crude Monte Carlo for our
    specific function f(x) on the range x=0 to x=5.
    Notice that this bound is sufficient because f(x)
    approaches 0 at around PI.
    Args:
    - num_samples (float) : number of samples
    Return:
    - Crude Monte Carlo estimation (float)
    
    """
    lower_bound = 0
    upper_bound = 5
    
    sum_of_samples = 0
    for i in range(num_samples):
        x = get_rand_number(lower_bound, upper_bound)
        sum_of_samples += f_of_x(x)
    
    return (upper_bound - lower_bound) * float(sum_of_samples/num_samples)