[Python] How to plot a one to many function on matplotlib in python

Very simple, if I plot x^2+y^2=z it makes this shape on python it will make this shape:



When I would like to plot it this way:



Below is my code, I am new so I copied it from the internet and have changed the line with the function to plot.

import matplotlib.pyplot as plt
import numpy as np
x = np.linspace(-4*np.pi,4*np.pi,50)
y = np.linspace(-4*np.pi,4*np.pi,50)
z = x**2+y**2
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot(x,y,z)
plt.show()


Also, how do I make it more high definition and smooth, this is a graph of z=sin(x)



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