Help!!

Why do the first two of the following 4 examples not work in Maple 15?

subs(m=21,`mod`(m, 4));
subs(m=21,m mod(4));
                               21
                               21
`mod`(21, 4);
21 mod(4);

                               1
                               1
Is there a (simple) workaround?

Thanks.

I've got a very complicated integral, generated by Maple (15), of the form:

Z:=a*Int(f(x),x=0..1);

I need to do some manipulations on the integrand.  So, I perform the following:

f(x)=GetIntegrand(Z);

f1:=perform operations on f(x)...etc

Z1:=a*Int(f1,x=0..1);

The trouble arises because sometimes Maple writes Z as shown above, and sometimes it writes it as:

Z:=-a*Int(-f(x),x=0..1);

and you can run the program twice in a row and you will get either form, randomly. So, sometimes Z1 will be wrong by a minus sign because you can't predict whether the minus sign is going to be embedded or not.

I've been complaining about this Maple property for years, to deaf ears within MapleSoft who insist it is not an issue, and it has been the subject of long discussions on this site that go nowhere.

So, the question becomes - how do I reliably extract the expression "a" from the expression for "Z" and how do I test whether it has a minus sign embedded within it, or explicitly showing.

This can drive you crazy if you are trying to do a calculation or write a program that always works.

Is there any simple way to print the sum of a series with exceptions?

For example, the following works (sort of), but its not consistent with mathematical notation, where one would expect to see something like a Sigma^' printed out, and the condition, alongw ith ther limits appear under the Sigma sign:

[Sum(1/(k^2-p),k=0..infinity),And(k<>p)]

I have two equations that are valid under the substitution sin <-> cos, so a simple way to generate the second equation is to replace all occurrences of sin with cos. But Maple gets the wrong answer when I do this, because of its built-in simplification. Here is an example. Z1 and Y1 shows the problem; Z2 and Y2 shows that my attempt to overcome the problem doesn't work.  Z3 doesn't work either, proving that the problem is internally generated by Maple because Maple insists on ordering variables in its own way, no matter how I write them.

________simplified example from Maple 15

restart;
Z1:=sin(-a*x+b);
Z2:='sin(-a*x+b)';
Z3:=sin(b-a*x);



                         -sin(a x - b)
                         sin(-a x + b)
                         -sin(a x - b)
Y1:=subs(sin=cos,Z1);
Y2:=subs(sin=cos,Z2);


                         -cos(a x - b)
                         -cos(a x - b)
 correct answer should be cos(-a*x+b) but the calculated results are off by a minus sign.

Ans1:=evalf(subs(a=1,b=2,x=3,[Y1,Y2,cos(-a*x+b)]));
          [-0.5403023059, -0.5403023059, 0.5403023059]

Question: How do I override Maple's desire to stick the "-" sign outside the sin function?

Why does the following statement not evaluate, or better yet, how can I make it do so?

A:=value(floor(p)) assuming p>0,p<1,p::real;

or

A:=simplify(floor(p)) assuming p>0,p<1,p::real;

or any one of a lot of different attempts along the above lines, all of which seem (to me) that they should yield

A:=0

rather than

A:=floor(p)

which is what I get.

Thanks in advance