human
I am working on the file "Homeworks/APPM5630_HW8_helper.ipynb".
The first task is:
One solution
Below is one way to use a class to do this
I'm not a software developer in python, so there may be much nicer ways, but this ought to be good enough.  There are many variants and extensions you can do, and of course, if you wanted to record some error function (like if you knew the true answer $x^\star$ and wanted to record $\|x-x^\star\|$ every iteration), you could easily incorporate that too.
Can you write Python program for it?
assistant
#Here is the Python program you requested.

f = lambda x : x**2

class fcn:
  def __init__(self):
    self.history = []

  def evaluate(self,x):
    # Whatever objective function you're implementing
    # This also sees objective in the parent workspace,
    # so you can just call those
    fx = f(x)
    self.history.append(fx)
    return fx
  
  def reset(self):
    self.history = []

objective = fcn()
F = lambda x : objective.evaluate(x) # alternatively, have your class return a function
x = mySimpleSolver( F, 1 )
print(x)