I have inserted a table of 4 rows and 2 columns after executing:

y:=x->x^2;

Then I have inserted prompts in each cell in 2nd to 4th row with Ctrl-J, like in the image of the section "Execution Order Dependency". On the left column  the  input  are numbers  (eg  2;)  and on the  right column y(%); (selecting  in Table properties  "Execution  ordering by rows ")

Then executed the whole worksheet (!!!) obtaining the desired output. Finally I have followed the steps in the section "Table of Values" for hiding input, and added the labels "x" and "y" in the first row.

If this is the intended way of doing it, I do not find this kind of tables an attractive option.

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of the calculation and then everything will work fine.

with(Maplets[Elements]):
f:=x->x^2:
L:=[seq([i,f(i)],i=1..3)]:
maplet1 := Maplet([
   BoxCell(Table([x, f(x)], L), 'as_needed'),
   Button("OK", Shutdown())
]):
Maplets[Display](maplet1);

There are several ways to use 'assuming' and cut down typing if it will be repeatedly used. One way, useful here, is:

Z:=SetOf(integer):
sin(n*Pi) assuming n in Z;

-2;`≤`x;`≤`;2;

Yes, there is a bug here in the conversion to gif, apparently for some expressions of type `+`. A workaround seems to be to convert each term individually:

x^2;-1/4*k^2;=0

<maple>x^2;</maple><maple>-1/4*k^2;</maple><maple>=0 </maple>

Right click on the picture. Select properties opens "Element properties", and "Alternate text" shows:

(1-x^2)*diff(y(x),x$2)-2*x*diff(y(x),x$1)-(k^2/(1-x^2)-j*(j+1))*y(x)=0;

 The server seems to be mapleoracles.maplesoft.com

Eg. using the Standard Units environment. See:

?Standard,trig

with(Units[Standard]):
plot(sin(x*Unit('deg')),x=0..180);
 

(u,v,w)... x = u*cos(v)*sin(w) y = u*sin(v)*sin(w) z = u*cos(w)

(u,v,w) ... x = u*cos(w)*sin(v) y = u*sin(w)*sin(v) z = u*cos(v)

(r,theta,phi) ...distance from the origin, r... theta is the counterclockwise angle measured from the x-axis in the x-y plane. phi is the angle measured from the positive z-axis, or the colatitude.

(r, theta, phi) = spherical coordinates (_r, _theta, _phi) = spherical unit vectors

_i = (sin(theta)*cos(phi)*_r + cos(theta)*cos(phi)*_theta -sin(phi)*_phi) _j = (sin(theta)*sin(phi)*_r + cos(theta)*sin(phi)*_theta + cos(phi)*_phi) _k = (cos(theta)*_r - sin(theta)*_theta)

...spherical coordinates (r,theta,phi)

(r, phi, theta)... x=r*sin(phi)*cos(theta) y=r*sin(phi)*sin(theta) z=r*cos(phi)

I suppose the problem is that after the assignment Maple forgets the assumption a>0(?). Is there a way to make _real_ assumptions on variables, which Maple will not forget and possibly warn me if I try to violate?