@farah adanan Probably you have not fixed everything. Save your worksheet in which the error occurs and load a link to it here using the bold green up-arrow in the mapleprime's editor. I'll check.

@Markiyan Hirnyk  Obviously the reason is in  rational  option. Examples show that in a solidly filled region the function takes complex values.
Look at these simple examples:

plots:-implicitplot(sqrt(-x^2-y^2), x=0..1,y=0..1);
plots:-implicitplot(sqrt(-x^2-y^2), x=0..1,y=0..1, rational);
plots:-implicitplot(sqrt(-x^2-y^2), x=0..1,y=0..1, gridrefine=2, rational);
 

@nm  The reason is probably in this:

whattype(1/sqrt(x));
op(1/sqrt(x));
                                                

A workaround:

expr:=1/sqrt(x)+sqrt(x);    
subs([x^(1/2)=abs(x)^(1/2), x^(-1/2)=(abs(x))^(-1/2)], expr);
                                           

 

@digerdiga  Yes. Here is an example:

simplify(sqrt((R-sqrt(R^2+z^2))^2));
simplify(sqrt((R-sqrt(R^2+z^2))^2))  assuming R-sqrt(R^2+z^2)<=0;
                              

@davtrs  This works. I added different colors to your lines.

Download Plot_problem_new.mw

@Carl Love I just thought  D(x)  was just a name, for example:

D(x):=5:
D(x);
                                     5

@vv 

In the original code I replaced  0.5  by  1/2 :
is(D(x)=DD(x));
                                        true

@whtitefall  Due to the parity of the integrand function, the answer to your question can be given without any computation  x=0 . Unfortunately, it seems that you have not understood my answer at all and again you have a lot of mistakes in your code.

@kuwait1  If we plot the expression in the denominator (without a power), it is clearly seen that it takes not only positive but also negative and zero values. Therefore, you should think about the adequacy of this model.

restart;
a := 2: Q := 5.48: d := 2.48: chi := (1/4)*Pi: phi := 0.: p := 5/2:
Expr:=(a*sin(X)*sin(phi)+d*cos(chi))^2+(a*cos(X)+d*sin(chi))^2+2*Q*((a*sin(X)*sin(phi)+d*cos(chi))^2+(a*cos(X)+d*sin(chi))^2)^(1/2)*cos(beta);
plot3d(Expr, beta=0..2*Pi, X=0..Pi);

@Markiyan Hirnyk  Where is your code to get this result?

@Markiyan Hirnyk  The point was  for  p=7/2  not for  p=1

@nm  It's just a way to programmatically code some symbols and combine them. Of course, in the above case, we can write down  ell  instead of  `&ell;` , but in other cases this method will be useful. Here are a few examples:

`&Delta;x`;
`&pm;`;
`&pm;3`;
30^`&deg;`;
                                              

@Mariusz Iwaniuk  convert(n, 'base', beta)  command returns the digits in reverse order.
                             

@mmcdara  In fact, these syntaxes are correct and they are documented. See the help on these commands.

@Carl Love  for the useful information on the binary search.