I've got the following piecewise function :

(x^2+y^2)^(alpha).arcsin(y/x) if (x,y) are in [-pi/2,pi/2]

0, (x,y)=(0,0)

1. How do I plot this function taking the alpha variable and the piecewise construct into account?

2. How can I check for points of discontinuity, indifferentiability from the plot/function itself?

I'm trying to verify whether the result obtained from a recursive Legendre function that I defined is the same as that obtained from the function available in Maple.

The arguments for LegendreP() mentioned seem to be v,x where v is the algebraic expression's degree and x is the expression. I tried calling the function as LegendreP(6,x) since I am to obtain the value at n=6 but this statement is not giving me an output in return that I can use to compare.

Would I have to plot both functions in order to be able to compare them?

I need to convert a base 10 int(defined as num) to its base 3 format using a while loop. I would like to store the remainder of the num%3 to a list/sequence/array in maple. Now, if I were to use a sequence, I would need a pre-defined range. How do I solve this issue?

I've got a piece-wise function(for which I've made the procedure) f defined over x<=-1, -1<x<1 and x>=1 which I am trying to plot over the range of (-2,2). I've tried using plot(f,-2..2) but it doesn't show any curve. Should I add a few more parameters to plot()?

I've got the following lists :

list1:=[1, 5, 14, 30, 55, 91, 140, 204, 285, 385, 506, 650, 819, 1015,

1240, 1496, 1785, 2109, 2470, 2870]
list2:=[1, 5, 14, 30, 55, 91, 140, 204, 285, 385, 506, 650, 819, 1015,

1240, 1496, 1785, 2109, 2470, 2870]

each generated by a procedure I defined. I need to verify that they are equal, which is the case. However, when I tried to use the evalb function as well as a flag that I was updating during a loop, in both cases, I got 'false' as  the answer along with the error message: 

"error, final value in a for loop must be numeric or a character"

What I am doing wrong?