@Kitonum 

The region is not filled between  0<= alpha <= 1, only the region boundries are drawn. Is it possible to add filling effect of the region.  Please check above code with orientation = [60, 135] and clockwise rotation. Can we make front moving part filled with different color.

Thanks

@Kitonum 

I am trying to ratate the region bounded by y=x^2+1, x=0, and y=5 about x=-1. I am expecting a solid shape with cylinder in the middle. But the code generates a surface only (hollow shape). How can I add effect of a solid shape?

restart:
with(plots): with(plottools):
ax := spacecurve([-1, t, 0], t = -1 .. 6, color = red, thickness = 2, linestyle = dash):

s1 := animate(plot3d, [[(x+1)*cos(t)-1, x^2+1, -(x+1)*sin(t)], x = 0 .. 2, t = 0 .. alpha, style = surface, color = blue], alpha = 0 .. 2*Pi, frames = 100):

s2 := animate(plot3d, [[cos(t)-1, x^2+1, -sin(t)], x = 0 .. 2, t = 0 .. alpha, style = surface, color = blue], alpha = 0 .. 2*Pi, frames = 100):



display(ax, seq(s || i, i = 1 .. 2), scaling = constrained, lightmodel = light3, axes = normal, orientation = [60, 70], labels = [x, y, z]);

@Kitonum 

Thanks alot. I will try my other graphs.

@Doug Meade

I can plot both curves but don't know how to add colors and rotate.

@Doug Meade 

Thanks for the solution. But I am looking for different solution. I like to draw a solid region filled with some color, then would like to rotate the whole region around axis of rotation. In above case a disk is moving over the surface.

This question is not homework related, i think moderator has changed my original posting. I am learning.

@vv 

why do I need to cover cases for t<=-2 and t>=10?

is the result not ZERO?

@Carl Love 

I have attached the worksheet. But let me know how to copy and paste code as TEXT format.

Integral.mw

@Rouben Rostamian  

Thanks, this solution worked out.

@Carl Love 

Your solution is still giving me integral form, but worked out as  Rouben Rostamian 
  suggested.

@Carl Love 

yes, inttrans is not required. I posted part of my code and forgot to remove this.

I used NumericEventHandler to force the function takes ZERO at t=0.

Unfortunatelt, I lost the remote connection to my office machine and can't run the posted soultion.

@Rouben Rostamian  

Sorry for posting like this. I simply copied the code and pasted here.

How can I copy and paste from maple environment to get editable code as text?

@acer 

Thanks for the insight. They should include these properties in next version.

Another question,

how can I improve graph quality after exporting animated gif?

Right now the qulaity is not good.

@acer 

Thanks.

Is there any other version that provides the facility of scaling and paning programmatically?

@Kitonum 

Thanks for showing another option, I may use it some time. But I need animation from z=0 to z=N for my work.

I am looking for , how can we control animation speed and size of objetc using programming code?

Please check my previous post.