@JAMET Change root~(3,c) to iroot~(c,3). But note that most cases have no solution. If you include negative cubes, most will have a solution, but they'll take longer to find.

The commands option package and with(TestLibrary) are superfluous to your example. They don't cause any trouble here, but they are heavy-handed commands that (IMO) should be avoided when they're not needed.

All of the rounding modes mentioned by Tom, and other modes, are available in Maple through the environment variable Rounding. See help page ?Rounding.

So, with this, I believe that Maple can easily emulate the rounding behavior of any other software.

But the whole mathematical theory of rounding errors is built on the concept of "significant digits" which is akin to "relative error" but is less well related to "digits after the decimal place" (which is akin to "absolute error".)

I am eager to see the results of applying this idea to your graph, which has far more degree-2 nodes than any randomly generated graph of the same order and size.

@JAMET In order for me to diagnose the problem, you'll need to upload as an attached file an executed worksheet showing the error message. Use the green uparrow on the toolbar.

The most likely culprit is that you haven't correctly transcribed the line found:= false;.

@JAMET If you're truly using Maple 2018 like your header says, this shouldn't make a difference, but try changing add(c) to add(x, x= c).

@JAMET Put your Replies after the Answer that they pertain to.

@JAMET The code above will only run in 1D input.

@dingtianlidi It's true that some first-year calculus textbooks give an simplified definition of limit that requires that the function be defined in some open interval containing the limiting value of the independent variable (except possibly at that limiting value itself). If this is the definition that you follow, then it's true that the limit doesn't exist. However, this is not the traditional definition, which allows the domain D of the function to be completely arbitrary.

@dingtianlidi The precise traditional epsilon-delta definition of limit is given on this Wikipedia page. See the section "Precise statement for real-valued functions". Notice that it allows the domain D of the function to be completely arbitrary. In particular the function may be undefined at an infinite number of points in every neighborhood of the limiting value of the independent variable.

@anthonyfl Regardless of whether you explicitly use coords= cylindrical (as I did), or explicitly use the coordinate transformations {z= r*cos(theta), x= r*sin(theta), y=y} as Kitonum and Acer did, and regardless of whether you want shells or washers, doing these animations requires that you "think" in cylindrical coordinates. Doing the integrals, however, doesn't require sophisticated 3-D thinking.

There is no attached file to your Question. Please try attaching again.

This comment is unrelated to your Question: Why do you want to do a log plot (as opposed to a regular plot) over such a small range? The total variation of the t-axis is only 1.52/1.4 = 9%.

@Anthrazit The command trunc is better than round for this purpose because it's built-in. 

How many nodes have degree 2?