You could try something like this:
restart;
f1 := alpha*(3*lambda^3*rho*d/(rho^2 + d^2)^(5/2));
I1 := int(f1,rho=a..b) assuming d>0;
d := 3.0;
I1;
Hope this helps.
J. Tarr

Tried your long equation with Maple 11.01 and Maple 10.06 and both gave
Groebner[Basis]( the_ideal, tdeg(x0,x1,x2,x3,y0,y1,y2,y3)) = [1]
Hope this helps.
J. Tarr

Yes, the plots obtained by running the worksheet that you uploaded at http://www.mapleprimes.com/files/5475_070922_Example.mw are completely different from the image that you posted at http://www.mapleprimes.com/files/5475_Example-Maple-Bug.jpg
May I suggest that you download your worksheet from MaplePrimes, preface it with a restart and run it. You will then be able to judge whether the plots are correct.
I suspect that something that comes before the part that you uploaded is causing the problem that you mentioned in your first post.
Good luck.
J. Tarr

Running your worksheet in Maple 9.03 and Maple 11.01, produces plots that show myQ_opt decreasing linearly with s until s=0.507 and then linearly with a smaller slope. The plot values also seem to accord with values for myQ_opt (0.9, 0.85 and 0.8) when s=0.2, 0.3 and 0.4.
Hope this helps.
J. Tarr

Could you upload your worksheet please? Someone should then be able to help you.
J. Tarr

Perhaps this is what you want ?MmaTranslator[Mma][FixedPoint].
Hope this helps.
J. Tarr

One Greek letter that you can't use is gamma (lower case) because Maple reserves it for Euler's constant - please see help page at ?initialconstants.
Since you prefer using the keyboard, you might consider using Maple's worksheet mode. This eliminates all pointy-clicky, but at the expense of a 1D input instead of 2D.
Hope this helps.
J. Tarr

You could try something like this
restart;
for n from 1 to 10 do
x:=2*n:
y:=3*n
end do;
Hope this helps
J. Tarr

Perhaps the best starting point for someone new to Maple's Units package is to choose Help and enter units. This brings up an introduction to the Units package that answers the questions you raise. After that you could search Help on Units,Index and Units,AddUnit, where you will find more detail.
Good luck,
J. Tarr

Maple's conventions for spherical coordinates are inconsistent. In the VectorCalculus package, it is as given by Thomas Madden above, and is defined in the help page at ?sphericalcoordinates, then choose definition.
The definition that Maple uses elsewhere, however, is shown at ?plot3d[coords], where you will find this:
*For spherical coordinates the interpretation is: plot3d(r(theta,phi), theta=a..b, phi=c..d,coords=spherical);
where theta is the counterclockwise angle measured from the x-axis in the x-y plane. phi is the angle measured from the positive z-axis, or the colatitude. These angles determine the direction from the origin while the distance from the origin, r, is a function of phi and theta.*
This is consistent with the conversion from spherical to cartesian shown at ?coords.
Hope this helps.
J. Tarr

You could try something like this:
restart;
eq1 := sin(x)=c+d;
eq2 := cos(x)=e+d;
eq3 := tan(x)=e;
sol := solve({eq1,eq2,eq3},[c,d,e,x]);
ans := op([1,1],(sol));
Then you could plot c,d,e like this:
assign(sol);
plot([c,d,e],x=-3/2..3/2,legend=["c","d","e"]);
Hope this helps.
J. Tarr

It looks as though Professor Robert Israel's help has been savaged by the dreaded < html tag. Perhaps he intended something on these lines,
restart;
with(VectorCalculus):
SetCoordinates(cartesian[x,y,z]);
hemisphere:= Surface(,phi = 0 .. Pi/2,theta = 0 .. 2*Pi,coords=spherical[r,phi,theta])
assuming r>0;
Flux(VectorField(, cartesian[x,y,z]), hemisphere);
J. Tarr

Perhaps you intended something like this?
restart;
F1:=y=piecewise(x>=0 and x<=50,0,x>=50 and x<=150, 150-x);
solve(F1);
Hope this helps.
J. Tarr

Your frustrations arise from the > and < symbols which can be interpreted as html tags. Before posting, click on input format below the text space and choose Plain Text.
Hope this helps.
J. Tarr

Your procedure runs OK for me on Maple 11.01, though there is a long list of Warning xxx implicitly declared local to procedure func. After declaring all these as local, the procedure runs OK, though it's not clear what you intend it to do.
Hope this helps,
J. Tarr