Here we want to define a function $$

of $$

and $$

coordinates:

$=$sin$$cos$(+)+$

where $=2+2$

$,$

and $$

are constants. We then plot the function with a colour map and make a histogram giving some details about the map. In particular, please do the following:

Introduce a Python function that does the following: $(1)$ defines Numpy arrays x and y from $$

to $$

with N elements each; $(2)$ computes the values of the function $$

as defined above; $(3)$ accepts $$

$,$

and $$

as arguments and $$

and $$

as keywords with default values $=1,=0$

; $(4)$ return arrays $$

$,$

and the $2$D Numpy array $$

$.$

Produce a figure with two panels side by side horisontally. The left hand side panel should show the colour map image and a contour plot $($on the same image$)$ of function $$

for $=1$

$,=1$

$,=100$

$,=0$

$,=2$

$.$ The right hand panel should show the histogram of the values of $$

for all the $(\backslash$times $$

$)$ pixels. Make sure that you plot looks professional, e$.$g$.,$ has labels and the title. Test that your code works for $$

between $0$ and $2.$

Compute and print in one line the mean of the function $(,)$

on the domain defined above. Use $.$format statement and the scientific notation with $4$ digits after the floating point.