Personally I think that it could get sticky if the numer,denom pair didn't do any normalization (and special cases could make life more difficult).

But here is a start for what I suspect you may be after:

I include an example with numeric coefficients, ie. a fraction. [edit] It splits rational fractions, suitably. Carl's Answer's original code did not do this.

Download numden.mw

I also wrote it so that the factors sin(z)^(-b+r)*cos(z)^(b-r) would get split (if present in the ostensible numerator, ie. unless they were also raised to a negative power), as the leading term is determined lexicographically. Replace the sign business with a check for positive if you prefer. Ie,

proc(ee::`*`) local c,n,d;
       (n,d) := selectremove(e->not type(e,`^`) or op(2,e)::positive,ee):
       c := frontend(content,[n],[{`*`},{}]);
       n*denom(c), denom(c)/d;
end proc:

It's not clear to me what kind of 2D plots you want. So I will make a wild/creative stab at it.

Perhaps you would like an animation of the contour plots (level curves on the 3D surfaces for y evaluated at each k value). Perhaps you will see an idea in the following (with contour lines only, or filledregions).

(The odd piecewise used in creating the 3D surface plots is there just so that all the surfaces will have a disconnected point at the maximal height, so that they all use the same range for the y-gradient colorscheme.)

cont_anim_idea.mw

You can simply use the add command.

Download Untitled_ac.mw

I'm not sure whether this will be of partial use.

The idea is that the 2nd column of the Matrix does better than the 3rd.

Download ext_ascii.mw

I do not know whether the expression V below is right, because I do not know whether this substitution for 0.6 in your M is right, or even whether M is right. (It may not agree with what Reuben has mentioned.)

I replaced 0.6 (which presumably stands in for a/L) with the parameter name p.

But this may still show you some numeric rootfinding and related plotting methods.

Download par_roots.mw

In my Maple 2015 it appears as if the numpoints option of SurfaceOfRevolution is only controlling the values used for the (blue) function curve, whose appearance you have suppressed by passing the showfunction=false option.

And since that detail also appears to be controlled (overridden) by the functionoptions choice, then I don't really see much merit in how it uses the numpoints option.

I do see an effect from the following, however, by temporarily adjusting the "default" for the grid option.

(I suspect that you may find that the grid values get used for the number of points used for the independent parameters in cylindrical coordinates. Hence they may serve the natural purposes.)

Again, this is in Maple 2015.

Download Surface0fRevolution_ac.mw

Member vv's nice method of substitution of the floor call by a name might be modifed, so that isolve finds integer solutions for the dummy name rather than having to pepper the new formula with values from an ad hoc range.

It handles at least these two examples, with only one substitution equation. I'm sure that it could benefit from robustification.

I displayed the intermediate piecewise result, since it helps illustrate how some progress was made (you could also evalf that piecewise, to see it even more clearly).

Download solve_uni_floor.mw

Another choice -- if you want to rotate each figure separately -- is to use the viewpoint option.

And, once again, a crude way to slow down the animation (including its gif export) is to repeat frames.

You might want to consider a single color (with glossiness and lighting) instead of shading=zhue, if you plan on exporting to .gif format.

Download FiguresEspace_ac.mw

The extrusion is done using POLYGONS substructures (rather than GRID or MESH, say), so I don't think that you would be able to get a surface with wireframe grid directly.

You can use overrideoption to get various other styles that are relevant for POLYGONS, though. This affects the CURVES as well as the POLYGONS.

You could use subsindets if you wanted to target just the POLYGONS and leave the CURVES alone (if your choice would be valid for them and otherwise alter them).
 

Download extrude_style.mw

Here I've re-used the code from the MathApp itself so as to retain the aspect ratios and relative placement per frame (and a scaling procedure PP to unify the frame view).

One of the few changes I made was to allow the randomize seed to be passed to the Reset procedure, which affects the shuffling randomization of the colors.

Download fib_anim.mw

I used repeated frames to slow it down. If you have a animated .gif player which allows you to adjust the speed then there's no need to use repeated frames.

Another possibility for your Maple 13 is to transform a result from odeplot using your known procedure FAK.

You could do that in one line (or in two steps, if you want to save the intermediate plot).

In older versions such as yours the odeplot curve renders thinly in places, which you may be able to make up for using the refine=1 option (which Preben also utilized).

(Although, for your given FAK, Preben's solution to utilize piecewise seems much more sensible.)
 

Download odeplot_actest.mw

Here are various versions, with the rest in black (rather than just default blue for output), or background effects as in the original question, etc.

Mix and match as wanted.

note: In the actual Maple GUI the 2nd and 3rd versions below render properly with the 5's having white foreground as well as the red background. Mapleprimes' backend doesn't render them properly.

Download mathcoloring.mw

You can scale the frames to a common x-y range, so that the conventional  animation (from plots:-animate, or collection displayed with the insequence option) renders them more like the Explore frames.

FractalesAnim_ac.mw

For example, using procedure PP to scale all the frames to [0..1]x[0..1],

PP := proc(P)
  local data,xmin,xmax,ymin,ymax;
  data := indets(P, Array)[1];
  xmin,xmax := [min,max](data[..,1])[];
  ymin,ymax := [min,max](data[..,2])[];
  plottools:-transform((x,y)->[(x-xmin)/(xmax-xmin),
                               (y-ymin)/(ymax-ymin)])(P);
end proc:

plots:-display(
  seq(PP(Fractals:-LSystem:-LSystemExamples:-PlotExample(
           Fractals:-LSystem:-LSystemExamples:-KochCurve,a))$5,
      a=1..5),insequence);

plots:-display(
  seq(PP(Fractals:-LSystem:-LSystemExamples:-PlotExample(
           Fractals:-LSystem:-LSystemExamples:-Carpet,a))$5,
      a=1..4),insequence);

plots:-display(
  seq(PP(Fractals:-LSystem:-LSystemExamples:-PlotExample(
           Fractals:-LSystem:-LSystemExamples:-Rings,a))$5,
      a=1..4),insequence);

plots:-display(
  seq(PP(Fractals:-LSystem:-LSystemExamples:-PlotExample(
           Fractals:-LSystem:-LSystemExamples:-Seaweed,a))$5,
      a=1..4),insequence);

plots:-display(
  seq(PP(Fractals:-LSystem:-LSystemExamples:-PlotExample(
           Fractals:-LSystem:-LSystemExamples:-GosperCurve,a))$4,
      a=1..5),insequence);

The most likely scenario is that procedure X called searchtext with invalid arguments by mistake -- in other words, a buggy situation overlooked by whoever wrote procedure X.

There are some other variations on the theme (eg. rethrowing errors of a similar sort, but made at a deeper level).

But it's difficult to say for sure, because you have, unhelpfully, omitted the example in which this arose.

It is not clear from you description what you are trying to do. Is it something like either of these?

Download fitting_ac.mw