I'm trying to evaluate this triple integral in the rectangular coordinate system and Maple appears to be stuck after the second iterated integral. I then tried to evaluate the same integral in another computer algebra system and got the answer almost instantaneously. My guess is that system converted it to an integral in the cylindrical coordinate system. Why does Maple not do the same? Is there a way to force Maple to do so without manually doing the conversion? I hope there isn't a typo that I'm missing.

I am looking at various ways to generate surfaces in a cylindrical coordinate system. When using the cylinderplot( ) command, the default color scheme is acceptable. However, when using the implicitplot3d( ) command, the surface comes out very dark. I've played with a few color/lighting options, but I'm still not able to have the implicit3d plot look anything like the cylinder plot. Can someone suggest any color/lighting/shading options that might acheive this. My initial results are attached.

In trying to obtain the closed form for the nth partial sum for some fairly basic telescoping series. It appears that SumTools[DefiniteSum][Telescoping] works well for rational summands. However, when the same is attempted on summands that are not rational, it fails. Below are a few examples.

For a function of one variable, I use the map command quite a bit to evaluate the function at several values of the independent variable. For example,

f:=x->x^2:

xlist:=[1,2,3]:

map(f,xlist)

How may I do something similar for a function of two variables? For example,

f:=(x,y)->x^2+y^2:

xylist:=[[1,1],[1,2],[2,1],[2,2]]:

Can the map command be used to evaluate f at each ordered pair? Maybe I'm not even using the correct data structure. Thanks!

Can anyone explain the inconsistency in the following?