I get:

with(Units:-Standard):
UseSystem(AddSystem(SI,degree[angle])):
sin(Unit(30*arcdeg));

                                 1/2

arcsin(sin(Unit(30*arcdeg)));

                                  Pi
                                 ----
                                  6

I would have expected in this context 30 [arcdeg] or something like that.

May be, or may be waves, or may be that design issues lay in some recent threads but nobody knowledgeable was there to take and discuss them (a more active and open minded attitude from the Maplesoft side would also help).

But in any case, I have some posts here and here that remains unreplied. I  do not know how challenging it could be for you but I would like to know an answer. Indeed, I could post on several more "challenges".

This is an elementary version:

with(Maplets[Elements]):
maplet1 := Maplet([
BoxCell(Table([variable, value], 
[evaln,eval]~([anames(user)])), 'as_needed'),
Button("OK", Shutdown()) ]):
Maplets[Display](maplet1);

This is an elementary version:

with(Maplets[Elements]):
maplet1 := Maplet([
BoxCell(Table([variable, value], 
[evaln,eval]~([anames(user)])), 'as_needed'),
Button("OK", Shutdown()) ]):
Maplets[Display](maplet1);

May be because the plot produced by this command in Maple 11.02 Standard is quite ugly:

May be because the plot produced by this command in Maple 11.02 Standard is quite ugly:

For that system it can be used:

op([1,3],PDEtools[casesplit]({de1,de2},[y1,y2]));
                                / 3          \
                                |d           |
                                |--- y2(x, y)| c2 c3
                  3             |  3         |
                 d              \dy          /
                 --- y2(x, y) = --------------------
                   3                   c1 c4
                 dx

op([1,3],PDEtools[casesplit]({de1,de2},[y2,y1]));

                                   / 3          \
                                   |d           |
                                c3 |--- y1(x, y)| c2
                  3                |  3         |
                 d                 \dy          /
                 --- y1(x, y) = --------------------
                   3                   c1 c4
                 dx

For that system it can be used:

op([1,3],PDEtools[casesplit]({de1,de2},[y1,y2]));
                                / 3          \
                                |d           |
                                |--- y2(x, y)| c2 c3
                  3             |  3         |
                 d              \dy          /
                 --- y2(x, y) = --------------------
                   3                   c1 c4
                 dx

op([1,3],PDEtools[casesplit]({de1,de2},[y2,y1]));

                                   / 3          \
                                   |d           |
                                c3 |--- y1(x, y)| c2
                  3                |  3         |
                 d                 \dy          /
                 --- y1(x, y) = --------------------
                   3                   c1 c4
                 dx

The workaround proposed by Robert works fine in Classic GUI and Standard GUI with typesetting set to extended, like by executing:

interface(typesetting=extended):

It works "wrong" in Standard GUI with typesetting set to standard.

The workaround proposed by Robert works fine in Classic GUI and Standard GUI with typesetting set to extended, like by executing:

interface(typesetting=extended):

It works "wrong" in Standard GUI with typesetting set to standard.

Another thing that you can do is replace "1" with "n" (any name), like:

a*x^(-n) + b*x^(-2*n);

                            (-n)      (-2 n)
                         a x     + b x

and substitute n by 1 at the end of the calculations. In Maple it is impossible to avoid the operation of the automatic simplification. I note that this is possible in Maxima by setting the flag simp:false:

simp:false$

a*x^(-1) + b*x^(-2);
	a*x^(-1)+b*x^(-2)

1+1;
	1+1

Another thing that you can do is replace "1" with "n" (any name), like:

a*x^(-n) + b*x^(-2*n);

                            (-n)      (-2 n)
                         a x     + b x

and substitute n by 1 at the end of the calculations. In Maple it is impossible to avoid the operation of the automatic simplification. I note that this is possible in Maxima by setting the flag simp:false:

simp:false$

a*x^(-1) + b*x^(-2);
	a*x^(-1)+b*x^(-2)

1+1;
	1+1

As the Bessel functions are oscillatory, there are many real solutions for y>=max(x,r^2*x). In a plot, for r=0.5:

eq := ((2*y*(y/r^2-x)^0.5*BesselJ(1,(y/r^2-x)^0.5)*
BesselJ(1,(y-x)^0.5))-((y-2*x)^2*BesselJ(0,(y/r^2-x)^0.5)*
BesselJ(1,(y-x)^0.5))-(4*x*(y/r^2-x)^0.5*(y-x)^0.5*
BesselJ(1,(y/r^2-x)^0.5)*BesselJ(0,(y-x)^0.5)))=0:

plots:-implicitplot(subs(r=.5,eq),x=0..100,y=0..100,gridrefine=2);

As the Bessel functions are oscillatory, there are many real solutions for y>=max(x,r^2*x). In a plot, for r=0.5:

eq := ((2*y*(y/r^2-x)^0.5*BesselJ(1,(y/r^2-x)^0.5)*
BesselJ(1,(y-x)^0.5))-((y-2*x)^2*BesselJ(0,(y/r^2-x)^0.5)*
BesselJ(1,(y-x)^0.5))-(4*x*(y/r^2-x)^0.5*(y-x)^0.5*
BesselJ(1,(y/r^2-x)^0.5)*BesselJ(0,(y-x)^0.5)))=0:

plots:-implicitplot(subs(r=.5,eq),x=0..100,y=0..100,gridrefine=2);

Yes, but the problem is that the Classic version of the help database suffers of second rate maintenance. Paradoxically, this is on occasions an advantage, as some bugs introduced to the Standard version sometimes do not affect it.

So, depending on the case I check Classic, Standard or both.

For periods I have experienced different variations of Standard GUI help browser freeze after one or a few searches (under Win XP). Though not a reproducible process, I have met periods when it became more and more acute along them, meaning that a larger fraction of searches ended in a help browser freeze as days pass. And strangely, whithout any change in the Maple instalation itself.  For example this was the case with Maple 13.00 until I have installed the 13.01 patch. After that, the situation improved to more tolerable levels.

Just a speculation, but I cannot avoid thinking about the cause as clashes between Java and Windows.