# include all necessary import statements here

# function shifting problem
def shift_function(f, a, b, n=401):
    """ 'f' is a callable funciton, 'a' and 'b' are
    the limits of the interval you want to consider."""
    pass

# plotting for the example in the function shifting problem
def funcplot(f, a, b, n=401):
    """ Constructs and plots the example given in the
    problem on shifting the domain of a function to [-1, 1].
    'n' is the number of points to use to generate the plot."""
    pass

# example in the function shifting problem
def shift_example(n=401):
    """ Plot the example given in the function shifting problem."""
    pass

# integral estimation problem
def estimate_integral(f, a, b, points, weights):
    """ Estimate the value of an integral given
    the function 'f', the interval bounds 'a' and 'b',
    the nodes to use for sampling, and their
    corresponding weights."""
    pass

# Jacobi construction problem
def construct_jacobi(a, b, c):
    """ Construct the Jacobi matrix given the
    sequences 'a', 'b', and 'c' from the 
    three term recurrence relation."""
    pass

# points and weights problem
def points_and_weights(n):
    """ Find the set of 'n' nodes and their
    corresponding weights for the interval [-1, 1]."""
    pass

# normal distribution cdf problem
def normal_cdf(x):
    """Compute the CDF of the standard normal
    distribution at the point 'x'."""
    pass
