@ahmeng  See help on  value(%)  and  emptysymbol(``)

@Lali_miani  In Maple, there is a rule: if at least one number is represented as a decimal fraction, for example  0.2  in your example, then Maple calculates the entire expression approximately (by default with 10 significant digits). If you want to have a symbolic representation, then instead of 0.2 you should write 1/5, that is  sin(1/5) . But then in the output Maple just writes the same thing, since sin(1/5)  can not be exactly written in a simpler form, for example, in radicals. But with this expression it is possible to work further, for example to calculate it approximately with some accuracy or to expand in a series, etc.

@Lali_miani  Unfortunately I'm not familiar with English-language books on Maple (English is not my native language). Maybe someone else will advise you a good book on Maple.

@Carl Love  But by this we have total 3 significant digits, rather than 3 digits after the decimal point:

interface(displayprecision= 3):
evalf(Pi);
                                                    3.14
 

@vv  Thanks for this effective way (I did not know about it before). In addition to your answer here is a quote from the Help: "To compute  i^n mod m where  i  is an integer, it is undesirable to use this "obvious" syntax because the powering will be performed first over the integers (possibly resulting in a very large integer) before reduction modulo m. Rather, the inert operator  &^  should be used:  i &^ n mod m .  In the latter form, the powering will be performed intelligently by the mod operation. 

@Joe Riel  It's better. I'm used to using this syntax for lists, but for vectors it also works.

@ahlamsaqer  Write here your specific function.

@Adam Ledger  See an implementation of your formula in the update of my answer above.

@Adam Ledger  Because he has Maple 7 only. Here is the text of this code:

restart:
# # # # # # # # # # # # # # # # # # # # # # # # # # # # 
# Differences in the various "functions"
# # # # # # # # # # # # # # # # # # # # # # # # # # # # 

printf("Consider the folowing:\nf:=x^2+5*x:\ng:=x->x^2+5*x:\nh(x):=x^2+5*x:\n\n");
f:=x^2+5*x:
printf("f is of type %a\n",whattype(f));
g:=x->x^2+5*x:
printf("g is of type %a\n",whattype(g));
h(x):=x^2+5*x:
printf("h is of type %a\n",whattype(h));
printf("subs(x=2, f) gives %a\n", subs(x=2,f));
subs(x=2,f);
printf("f(hello) appends (whatever) to x - %a\n",f(hello));
f(hello);  #appends (whatever) to x;
printf("subs(x=2, f) gives %a\n", subs(x=2,f));
printf("...but f(2) gives %a\n", f(2));
f(2);
printf("g(2) gives %a\n", g(2));
g(2);
printf("Both h(2) and eval(h(2)) give %a\n", eval(h(2)));
eval(h(2));
printf("...but rather subs(x=2,h(x)) gives %a\n", subs(x=2,h(x)));
subs(x=2,h(x));  

@brian bovril  My system is Windows 10, Maple 2017.3 32 bit. I have no more comments.

@torabi I do not understand what you mean by "other option".

Maybe you mean a numerical solution? In this case, you also get a zero solution:

restart;
sol := dsolve(eval({diff(r*(diff(u(r), r)), r)/r = 0, u(R0) = U2, u(h) = U1}, [h = 1, R0 = 5, U1 = 0, U2 = 0]),  numeric);

plots:-odeplot(sol, [r,u(r)], r = 1 .. 5, color=red, thickness=3);
 

@brian bovril  It works for me in Maple 2015.2, Maple 2016.2 and Maple 2017.3 properly. Try to do restart and run again.

PS. I uploaded your worksheet. Everything works as well.

@gmzsvsclk 

restart:
P:=product((x-j),j=0..11);
Q:=a*x^6+b*x^5+c*x^4+d*x^3+e*x^2+f*x+g:
R:=j*x^4+k*x^3+l*x^2+m*x+n:
T:=Q^2-R:
[seq(coeff(T,x^p)=coeff(P,x^p), p=1..12), coeff(T,x,0)=coeff(P,x,0)
];
solve(%);

Verification:

assign(%[1]):
'Q'=Q;
'R'=R;
solve(Q^2-R);

Edit.

@asa12  In Maple 12 replace the line  
S:=[seq(subs(var=~p,obj2), p=P)];
by the line
S:=[seq(subs(zip(`=`,var,p),obj2), p=P)];

As for other matrix transformations (in particular those you are writing about), other procedures or an extension of  IsEquivalent  procedure are needed.

@asa12  I did not understand the meaning of your question.