This issue is most likely a windows 7 issue.  It is not experienced in Maple 16.02 32bit Windows XP

You could use student[intercept] or intersection from the geometry package.

> assume(t::real);
> z := t = conjugate(a)*b+conjugate(c)*d;

> a := solve(z, a);

                                     ________
                                           _  
                                     -t~ + c d
                               a := ---------
                                        b    
> simplify(expand(expand(a)));

                                            _
                                   -t~ + c d
                                 - --------
                                      _    
                                      b    

> assume(t::real);
> z := t = conjugate(a)*b+conjugate(c)*d;
> a := solve(z, a);

                                     ________
                                             _  
                                     -t~ + c d
                               a := ---------
                                        b    
> simplify(expand(expand(a)));

                                              _
                                   -t~ + c d
                                 - --------
                                      _    
                                      b    

You could try

a:=display({P,f(C)})

animate(display,[a,orientation=[A,10]],A=0..360);

Yes it appears if one leaves out the multiplication sign in front of a bracket with a variable, it does not fully integrate.

In this case where he mentions it works

int(int(int(-(4-6*(x+z)+12*x*z)*y*(y-z)^3, x = 0 .. 1), y = 0 .. 1), z = 0 .. 1);

                                                       
If we take out the multiplication after the first y, it causes an unfinished integration when it tries to integrate y.

int(int(int(-(4-6*(x+z)+12*x*z)*y(y-z)^3, x = 0 .. 1), y = 0 .. 1), z = 0 .. 1);
                              

i think it is a bit early to say there is no way to increase the quality of the plots.  in mathematica there seems to be a lot of behind the scenes operations to enure plots please the user.  with, it seems, a reduction in accessibilty or experimentation with the created structure.

@_zgj Mathematica uses antialiasing -> true by default.  Set antialiasing->false and I think the plots will compare the same.

Hm, I don't think the equations are quite right. 

int(exp(sqrt(x^2+5)))

Has no symbolic answer.  Numerically I wouldn't know how to approximate it either.  I think you are stuck.

I removed one bracket and got this but until we determine where the missing bracket is no one will go further.

Your other line should also be rewritten to reflect the maple language

hj=int(int(int(int(prod2,x=0..a),y=0..b),alp=d1..d2),bet=k1..k2);

Sure, but there is no code translator.  You'll need to colaborate with someone who knows both systems.

What is the reason to translate Maple to Reduce?

Here it is as a procedure

Download Stem_leaf_plot_proce.mw

How about this?  Maybe someone can format the output to look better.

Download stem_leaf_plot.mw

The general guidance when using two commands that are the same from different packages which have been loaded is to use the long form command as you have done LinearAlgebra[Rank].  And as Carl has mentioned using the uses statement inside the procedure when calling out to commands inside packages.  Using with inside a procedure adds a lot of overhead which is generally not a good idea, not wrong, but just clunky programming.