"Your images here all look like Chinese error messages"

Thanks for your kind reminder. Sorry  I didn't notice it. Yes my images are linked from a Chinese site. In my computer, I don't find any difference of your image and mine.
You mean that all the images I posted are unreadable?

I am now trying the way you suggested.

Tell me if these images/animations are OK now? Thank you.

The following would work:

with(plots):
 r:=sin(3*t): 
 K:=30: for i from 1 to K do ti:=i*2*Pi/K:
 curve[i]:=polarplot(r(t), t=0..ti) od:
 C:=display(seq(curve[i],i=1..K), insequence=true):
 display(C, scaling=constrained,tickmarks=[0,0], thickness=3,insequence=true);

Yes, it works. Thank you.  Just use "insequence=true" twice.

The following would work:

with(plots):
 r:=sin(3*t): 
 K:=30: for i from 1 to K do ti:=i*2*Pi/K:
 curve[i]:=polarplot(r(t), t=0..ti) od:
 C:=display(seq(curve[i],i=1..K), insequence=true):
 display(C, scaling=constrained,tickmarks=[0,0], thickness=3,insequence=true);

Yes, it works. Thank you.  Just use "insequence=true" twice.

with(plots):with(plottools):

f:=x->x: g:=x->x^2:

F:=spacecurve([x,f(x),0],x=-0.2..1.2,color=blue, thickness=3):

G:=spacecurve([x,g(x),0],x=-0.2..1.2,color=red, thickness=3):

region:=plot3d([x,y,0],x=0..1,y=g(x)..f(x),color=grey, style=patchnogrid):

FG:=display(region,F,G,axes=normal, scaling=constrained):

transform((x,y,z)->[x,y,0])(FG);

The above will produce the graph:

But the following do not work (I use Maple 8):

with(plots):with(plottools):
f:=x->x: g:=x->x^2:
F:=spacecurve([x,f(x),0],x=-0.2..1.2,color=blue, thickness=3):
G:=spacecurve([x,g(x),0],x=-0.2..1.2,color=red, thickness=3):
region:=plot3d([x,y,0],x=0..1,y=g(x)..f(x),color=grey, style=patchnogrid):
FG:=display(region,F,G,axes=normal, scaling=constrained):
transform((x,y,z)->[x,y])(FG);

Plotting error, vertex requires three components
 

Thanks for your suggestion on using "Transfom", which I didn't know before.

Maybe you are using a new version of Maple?
 

I use Maple 8.

Maybe you are using a new version of Maple?
 

I use Maple 8.

But it doesn't work.

restart: with(plots):
animate(polarplot,[sin(3*t),t=0..x],x=0..Pi,thickness=3,frames=20);

Warning, the name changecoords has been redefined

Error, (in animate) bad range arguments: [sin(3*t), t = 0 .. x], x = 0 .. Pi

But it doesn't work.

restart: with(plots):
animate(polarplot,[sin(3*t),t=0..x],x=0..Pi,thickness=3,frames=20);

Warning, the name changecoords has been redefined

Error, (in animate) bad range arguments: [sin(3*t), t = 0 .. x], x = 0 .. Pi

Yes, it works.
But what is the difference between your codes and the first of mine?
Thanks

Yes, it works.
But what is the difference between your codes and the first of mine?
Thanks