@Carl Love 

I'm doing this, but I'm still get a different answer.

> restart:
> with(plots):
> params:= [m=6.3,Q1= 1]:
> Top_of_Q1:= maximize(eval((8*wx^2*(m-1)/(Pi^2*sqrt((m*wx^2-1)^2+Q1^2*wx^2*(wx^2-1)^2*(m-1)^2))), params));

                      Top_of_Q1 := .5730486817 I

...Even more confusing... Here I substituate by hand the values of m and Q and I get the same answer.

>restart:with(plots):
> a:=(8*wx^2*(6.3-1)/(Pi^2*sqrt((6.3*wx^2-1)^2+1^2*wx^2*(wx^2-1)^2*(6.3-1)^2)));

> semilogplot({a},wx=0.1..2,axes=boxed);

> Top_of_Q1:= maximize(eval((8*wx^2*(6.3-1)/(Pi^2*sqrt((6.3*wx^2-1)^2+1^2*wx^2*(wx^2-1)^2*(6.3-1)^2)))));

                      ...I don't understand why I'm geting a complex number

> 
>... I've reduced the expression to its minimum and I still get this answer. 

> restart:
> Top_of_Q1= maximize((((8*wx^2*(6.3-1)/(Pi^2*sqrt((6.3*wx^2-1)^2+1^2*wx^2*(wx^2-1)^2*(6.3-1)^2))))));

                      Top_of_Q1 = .5730486817 I

> 
 

@C_R 

...so I did reformulate the assignement to the following, but the output somehow off :

> restart:
> with(plots):
> params:=m=6.3,Q=1:
> Top_of_Q1=(maximize((subs(params,(8*wx^2*(m-1)/(Pi^2*sqrt((m*wx^2-1)^2+Q1^2*wx^2*(wx^2-1)^2*(m-1)^2)))))));
                                                10
                     Top_of_Q1 = .3409538241 10

@C_R 

Thank you for your help.

Unfortunately I'm still strugling with this.

If you don't mind I decided to piece meal this as I'm trying to understand what I am doing wrong. I made the following code : 

> restart:
> GainQ1=8*wx^2*(m-1)/(Pi^2*sqrt((m*wx^2-1)^2+Q1^2*wx^2*(wx^2-1)^2*(m-1)^2));
> params:= m= 6.3, Q1=1;
> a:=subs(params, GainQ1);
> Top_of_Q1 = maximize(a,wx=0.1...2);

The output I get is the following : 

Error, (in maximize) minimize expects its 2nd argument, vars, to be of type {name, set(name)}, but received wx = .1 .. 2
 
I'm not sure again wat I am doing wrong.

Thank you for the assistance.

@C_R 

Do you mean I shouldn't assign any range for wx?

wx=0.1..2