@Rouben Rostamian In Maple 2022, ?coords takes me to a very helpful page "Coordinate Systems Supported in Maple" which makes this clear. (This page wasn't so easy to find in the online help.):
"(**): There are two widely used conventions for how to represent spherical coordinates: one is used more in physics and the other more in mathematics. The only difference is a swap of the second and third coordinate: the vector represented by
"u, v, w"
in one convention is represented by
"u, w, v"
in the other. The plotting library, the changecoords command, and the VectorCalculus package allow you to use the coordinate system names spherical_math and spherical_physics to refer to these coordinate systems unambiguously. You can also use the name spherical; its behavior is as follows:
– If neither of the Physics and VectorCalculus packages has been loaded (using the with command), then the plotting library and the changecoords command will interpret spherical as spherical_math.
– If either of the packages Physics or VectorCalculus has been loaded, then the plotting library and the changecoords command will interpret spherical as spherical_physics.
The VectorCalculus package will always interpret spherical as spherical_physics.