If you really want to do it in a manner similar to your original posting, then something like this might work for you. I had to guess at the assignments to B12 and B13 as they apparently got chopped off in your original (posted as HTML rather than plaintext I surmise). B11:=x1<=B1 and x2<=B2; E11:=0; B12 := B1>=x1 and B2>=x2; E12 := simplify(int(int(x1-h1+x2-h2,h2=B2..x2),h1=B1..x1)); B13 := B1<=x1 and B2>=x2; E13:=simplify(int(int(x1-h1+x2-h2,h2=B2..U2),h1=B1..x1)); Eobj:= proc(X1,X2) local z; z := map(eval,`if`(B11,E11,0)) + map(eval,`if`(B12,E12,0)) + map(eval,`if`(B13,E13,0)); z := eval(z,{x1=X1,x2=X2}); end proc; B1:=0;U1:=1;B2:=0;U2:=1; eval(Eobj(x1,x2),[x1=-10,x2=-10]); Eobj(-10,-10); plot3d(Eobj,-10..10,-10..10); #plot3d(Eobj(x1,x2),x1=-10..10,x2=-10..10); I feel a bit guilty posting this, as it contains all manner of sins. And I'm not completely sure that it does what you intended. Also, notice that Eobj(x1,x2) will return something possibly useful to you while Eobj(a,b) will produce an error. You might be better off studying Robert's response and changing your approach accordingly. I have an idea that, even if the code above does do what you want, the reasons for it might appear confusing. acer

Could plots ever be passed back and forth from GUI to kernel? Would bidirectional communication of plot structures not allow for both programmatic and graphical interface (eg. mousy) access? Actually, why pass the whole structure back and forth, instead of some pointer to it? And, if that isn't a bad idea, then why wouldn't it have been done years ago? Couldn't this give the first glimpse of CAD functionality? Why can the user now annotate plots, but not get any programmatic access to those effects? acer

That's a quite correct and expected observation, no? In (1D) Maple Notation, the caption is not yet a typeset object. The kernel (even its parser) has not yet seen it. It gets handled in the usual way for Maple, which means that as an argument to plot() it is evaluated prior to being bound to any (local) formal parameter of plot(). The plot() routine does not have special evaluation rules, I believe. So evaluation (and automatic simplification too) are not preempted here. In 2D Math input, the toggling of parts of the caption as "atomic identifier" means that those contents aren't really Maple symbolics as they seem. The typesetter forms them (as something similar to MathML). But the resulting object cannot be manipulated by Maple as a mathematical symbolic object in that state. It's more like an inert piece of display mark-up. The Std GUI knows how to render it nicely, but Maple's kernel sees only a big, strange looking name, I suspect. And that's why one can use the atomic identifier trick to avoid evaluation or even automatic simplification, because the kernel just sees one big name. acer

Couldn't it be trickier than just normalization? What about linear combinations of eigenvectors associated with the "same" eigenvalue? If what's wanted are approximately the same results (across platforms, compilers, implementation platform, optimization flags, etc) then maybe that which will always suffice is always to choose some desired orthogonal basis, project, and normalize. acer

Fabulous. Thanks very much. I knew about that atomic identifier context-menu item, but I wouldn't have imagined to try it within the plot call. Its acting in-place on the input is what makes it work, it seems. It's obviously a very handy mechanism -- that in-place atomic identifier context-menu toggle -- so perhaps it could be more widely referenced in help-pages that refer to 2D Math. acer

I too would like to know the answer to this -- how to get the volume of revolution to be solidly filled. Maybe there is some simple answer. A good solution would be something that would truly look filled, were it transluscent. By that I mean that faking it (say, by assigning the VolumeOfRevolution plot to a variable and then displaying both that and two additional plots of the end-discs) would not always look truly filled. I had first imagined that the following command might do it, Student[Calculus1][VolumeOfRevolution](1/x, x=1 .. 2,axis= 'horizontal', volumeoptions=[filled=true], showfunction=false, 'distancefromaxis' = 0, 'output' = 'plot'); acer