I was setting up a worksheet for my vactor calculus class and tried to show how the DifferentialDiff command from the VectorCalculus package was limited.  I was expecting to have it give undefined or something similar for all directions with the function I am using.  Unfortunately, I got 0 when the directional derivative is truly undefined and I got undefined when the directional derivative is 0.

This is the code I am using.  Unfortunately, this site will not take the worksheet or plot the function for me.
 

with(VectorCalculus):
s := min(abs(x),abs(y));
plot3d(s,x=-1..1,y=-1..1);
DirectionalDiff(min(abs(x),abs(y)),<-1,1>,[x,y],point=<0,0>);

A person asked me why the following code does not give the integral of (x^2+y^2)*z over the top of the unit sphere.

VectorCalculus:-SurfaceInt((x^2 + y^2)*z, [x, y, z] = Surface(<1, s, t>, s = 0 .. Pi/2, t = 0 .. 2*Pi, coords = spherical))

The correct answer is Pi/2, but Maple gives 2*(-1 + Pi)*Pi^2.

Will someonoe please explain this behavior?

I was playing with plots:-fieldplot in Maple 2019 and found that sometime the grid option gives a strange result.  The code I used was

with(plots):
fieldplot([-x/(x^2+y^2)^1.5,-y/(x^2+y^2)^1.5],x=-1..1,y=-1..1);
fieldplot([-x/(x^2+y^2)^1.5,-y/(x^2+y^2)^1.5],x=-1..1,y=-1..1,grid=[8,8]);
fieldplot([-x/(x^2+y^2)^1.5,-y/(x^2+y^2)^1.5],x=-1..1,y=-1..1,grid=[7,7]);

The first two plots come out as expected.  The third plot has (0,0) in the grid, a point where the vector field does not exist.  Rather than giving an error or ignoring the point, Maple 2019 (and 2018) plots a single arrow through the origin. The file with plots is below.  I hope that this can be changed to give a different output.

Download fieldplots_1.mw

Does anyone know why png is not listed in the help on plot/devices?  The png device exists and works.

Also, are there any other unlisted plot devices?

I have a test server up for MapleTA 8.  Where is the option to show a student's name on the questions?