Here's how I see what you've tried.
You want to solve the position of the rocket, {X3,Y3,Z3}, out to 1 year's worth of 1-seconds (ie. problem is scaled so that independent variable t is in seconds).
The derivatives of the rocket's motion/position w.r.t will depend on the position of the two planets, {X,Y,Z} and {X1,Y1,Z1}.
Instead of building one large differential system to encapsulate all three objects (where only "influence" is of two upon the third) you instead solve each of the two planets' positions separately, using listprocedure output. Then you embed those resulting on-the-fly calls (to solve the planets' positions) into the differential equations for the rocket's motion/position. Doesn't that force maple to do more work than if the three systems were rolled up together?
You're using dsolve/numeric method=lsode throughout, a hard working (if somewhat antiquated) stiff solver. Is that the best idea here? (You may want routines for dX/dt, dX1/dt, etc, depending on how you go here.)
acer

Perhaps it was 16*x = y^2+4*z^2 that was meant instead?
acer

Vo/Vs isn't (technically) a subexpression of the original equation. But you can substitute for something like it, then isolate, and then substitute back again.
eval(normal(isolate(eval(Vs/R1=(Vs-Vo)/R2,Vo=Z*Vs),Z)),Z=Vo/Vs);
acer

eq1 := x^2+y^2+z^2=1:
eq2 := z=y:
# Now substitute eq2 into eq1.
neweq := eval(eq1,{eq2});
# You want a parametrization that has x=cos(t).
# But that forces what y (and z) must be. You can
# ask maple to solve for the y, after the
# substitution of x=cos(t).
eq_subsforx := eval(neweq,x=cos(t));
solve(eq_subsforx,y);
# Check, by substitution.
eval(neweq,{x=cos(t),y=sin(t)*sqrt(2)/2});
eval(eq1,{x=cos(t),y=sin(t)*sqrt(2)/2,z=sin(t)/sqrt(2)});
# Plots are another way to examine the results.
p1 := plots[implicitplot3d](eq1,x=-1..1,y=-1..1,z=-1..1,style=surface):
p2 := plots[implicitplot3d](eq2,x=-1..1,y=-1..1,z=-1..1,style=surface):
p3 := plots[intersectplot](eq1,eq2,x=-1..1,y=-1..1,z=-1..1):
plots[display]([p1,p2,p3],axes=boxed);
plots[spacecurve]([cos(t),sin(t)*sqrt(2)/2,sin(t)/sqrt(2),t=-0..2*Pi],axes=boxed);
acer

The copy() command should produce a copy of an Array along with the indexing function.
Eg, simply,
B := copy(A);
That should work for Array, Matrix, or Vector. It should also reproduce 'storage' and 'order'. The only thing that it does not reproduce, I believe, is the attribute readonly (which makes sense, to me, as I can't see why one would ever want two identical readonly objects).
acer

Did you mean to write,
Maximize(Payoff(Q, sval, pval, paval))
instead of,
Maximize(Payoff(Q, s*val, pval, paval))
Also, why go to the expense of defining procedure Payoff each time that Qopt2 is called? Actually, why use a procedure for the payoff altogether, instead of an expression?
I'm thinking that you could do it something more like this,
Payoff := proc(Q, s, p, pa)
1 - 1/24*s^3 - 1/2*s*min(1, Q + 1/2*s)^2 + 1/4*s^2*min(1, Q + 1/2*s)
- 1/3*min(1, Q + 1/2*pa)^3 + 1/3*min(1, Q + 1/2*s)^3
+ Q*min(1, Q + 1/2*pa)^2 - Q*min(1, Q + 1/2*s)^2
- Q^2*min(1, Q + 1/2*pa) + Q^2*min(1, Q + 1/2*s)
+ s*Q*min(1, Q + 1/2*s) - 1/2*pa + 1/2*pa*min(1, Q + 1/2*pa)^2
+ 1/4*pa^2 - 1/4*pa^2*min(1, Q + 1/2*pa) - s*Q + pa*Q
- pa*Q*min(1, Q + 1/2*pa) - p*Q;
end proc:
Payoffeq:=Payoff(Q, s, p, pa);
Qopt2 := proc(sval, pval, paval)
local eq, result;
global Payoffeq;
if not type({args},'set'(numeric)) then
return 'procname'('args');
end if;
eq := subs({s=sval,p=pval,pa=paval},Payoffeq);
result := Optimization:-Maximize(eq,Q=0..1);
if type(result,'list'({numeric,list})) then
return result[1];
else
return 'procname'(args);
end if;
end proc:
Qopt2(.2, 0.1e-1, 1);
plot('Qopt2'(s, 0.1e-1, 1),s=0.1..0.5);
You'd want to check that I didn't make any mistakes above, that the fornulae match, and that the results make sense, etc.
The results I get differ from yours, even when using Q_opt() on just single points and not plotting it. So, let's look at what the Payoff looks like for a particular set of the parameters.
plot(subs({s=0.2,p=0.1e-1,pa=1},Payoffeq),Q=0..2);
For those values, I see a maximum at just over 0.9. And that seems to agree with the procedures I've shown here, and not with Q_opt(.2, 0.1e-1, 1) which returned 0.7911 for me.
acer

Consider the slightly different call,
plot([Q_opt(0.1,0.01,0.5),Q_opt(0.2,0.01,0.5),Q_opt(0.3,0.01,0.5),Q_opt(0.4,0.01,0.5)],s=0..0.5,legend=["Actual value s=0.1","Actual value s=0.2","Actual value s=0.3","Actual value s=0.4"]);
Does it come out the same?
acer

Rewrite both fractions with a denominator of 18*19.
1/19 = (1/19)*1 = (1/19)*(18/18) = (1*18)/(19*18)
-5/18 = (-5/18)*1 = (-5/18)*(19/19) = (-5*19)/(18*19)
( 1*18 -5*19 )/(18*19)
acer

You can get input such as the greek letters to be typeset in 2D by using the command completion facility. This facility allows you to get a name completed by maple.
In Linux, command completion is accomplished by simultaneously pressing Ctrl-Shift-Spacebar.
For example, if I am in 2D Math input mode, and I type,
alph
then the partial input word underway (alph) will complete to the nice 2D typset greek letter alpha. It also seems to work just when the word's last letter has already been immediately entered by me (ie. when the font changes from italic to normal).
acer

All those 80 x[i] are strings, not numbers. So sum() can't add them up.
Try putting a parse() around the x[i_4]'s and x{i_5]'s, or use fscanf to read floats instead. There should be several ways to do it.
Also, you might help yourself if you use add() instead of sum() for simply adding up sums. (I suppose it may have come out of a palette.) And for this sort of work, and for learning programming in the Maple language, you might try 1D Maple input instead of 2D Math input, and Worksheet instead of Document.
acer

The help-page ?separator may provide some explanation.
acer

See the help-page ?Task,EquationOfLineBetweenTwo2DPoints
Or, run the command,
Student[Precalculus][LineTutor]();
acer

How many times do we have to see submitters' getting caught up with the less-than symbol, before the mapleprimes maintainers switch the default Input format to plaintext?
Most submitters are not using marked-up input. It's the new submitters who pay most here. The old hands would know better, if by default they had to toggle on Filtered HTML as the Input format.
acer

While it may require an extra step to use, mint may also assist with locating syntax errors.
On the one hand it may take an extra step to invoke, be that as a separate shell command or as use of a vi/emacs macro.
But I mention mint because it can do so much more, to help author large maple sources, and because not every user out there will have heard of it. I have always supposed that its name is a joke on `lint` (for C).
On Unix at least, mint is a program than sits in the bin.ZZZ directory alongside the `maple` and `xmaple` scripts. It has a help-page accessible within maple itself. It also comes with a man-page on Unix.
It can do a lot more than simple syntax checking, including reporting on undeclared locals, globals, dead code sections, and lots of other good stuff. The level of reporting can be fine-tuned, via options.
I find that mint is especially good for finding some sorts of coding mistakes that, while not syntax errors per se, can still come back and bite in unexpected ways.
While I'm showing my preference for the commandline Maple interface for managing larger programming jobs, I can also point out the very nice $include and $define directives. I have seen $include used both for module source layout (each local procedure gets its own $include in the module source defn file) and for injecting common code fragments.
acer

Let's try to create a customized refinement of the Atomic system of units, in which energy is simplified and displayed by default to keV, length to cm, area to cm^2, and volume to cm^3.
Units:-AddSystem(customAtomic,Units:-GetSystem(Atomic),cm,cm^2,cm^3,keV);
Units:-UseSystem(customAtomic);
Now to try and test that,
simplify(3.0*Unit(g)*Unit(mm)^2/Unit(s^2));
with(Units[Standard]):
T:=3.0*Unit(g)*Unit(mm)^2/Unit(s^2);
T/(1.1*3.0*Unit(g)*Unit(mm)/Unit(s^2));
T/(1.1*3.0*Unit(g)/Unit(s^2));
T/(1.1*3.0*Unit(g)*Unit(mm^(-1))/Unit(s^2));
acer