I have just made my first polar plot, but I am a little disappointed with the result.

Code
polarplot([(1+cos(x)^2)*(1/2), cos(x)], x = 0 .. (1/2)*Pi) 

Output

How can I remove that little gap between the grey line and the black line?

Hello, 

I have plotted a function f(e) vs. e (see code and figure). However, the graph looks jagged and nasty. I tried increasing the numpoint value but this doesn't seem to work (even at 50,000!). I'm fairly new to Maple and so I don't know any other commands/ tricks to help myself. 

Does anyone know how I smooth this plot?

Thanks.

Code: 

> f := (1+(73/24)*e^2+(37/96)*e^4)/(1-e^2)^(7/2);

Bear with, I'm a noob. This is my code so far:

    > ball := proc (x, y) plots[pointplot]([[x, y]], color = blue, symbol = solidcircle, symbolsize = 20) end proc;

    > animate(ball, [1+sin(t), 1-sin(t)], t = 0 .. 2*Pi, scaling = constrained, frames = 100);

I like the output I have but my aim is to have, say, 8 of these balls, all with their own trajectories, and animated on the same axis. All the trajectories would depend only on one parameter, t.

I've plotted this graph, but it's supposed to be smooth, any idea what's happened?

Hello,

I have the following object:

t = ∫ (from 0 to e_0) [1 + (121/304)e²)]^1181/2299 (1 - e²)^-3/2 e^29/19 de

and I would like to plot t vs. e_0 on the interval 0 <= e_0 <= about 0.9.

So far, I have managed to get Maple to integrate the thing for any value I like of e_0 from 0 up to (but not including) 1. So, I now just need to get Maple...