In this worksheet, how do the several successful plot commands evaluate the complex expression being plotted, and why do the unsuccessful plot commands fail to do so?

Plot_complex_expression.mw

The changecoords command in the procedure below executes the plots:-changecoords command despite the preceding unwith(plots) command.

How can I execute the non-plot version of the changecoords command in the procedure. It would be very inconvenient of all the various commented plot commands had to be preceded by plots:-

restart; with(plots):   # first command in the worksheet

  # many statements executing various plot commands

 
P := proc()

unwith(plots):

changecoords([x, y, z], [x, y, z], spherical):

with(plots):

end proc:

P();
Error, (in plots/changecoords) changecoords does not accept plot options or other additional arguments
 

  # many more statements executing various plot commands

 # last command in the worksheet

This worksheet animates stereographic projection of a grid on a sphere onto the plane the sphere sits on.

Is there a way to display matching colors in corresponding cells in the two grids?

Stereographic_projection.mw

EssayTools command SpellCorrectWord("trnu") will return "run" and not return "turn".

Is there a way for Maple to only find anagrams with the same length as the given string?

Can Maple do this referencing an external dictionary located on the internet e.g. a complete Websters?

The uploaded worksheet describes a chain driven at constant speed by gears.

What math will describe its shape?

GearDrivenChain.mw