@kelvin goh It should be g, not g(x). It should be undefined, not undefine.

Even by imposing various severe conditions on the parameters (such as k_1= 0, k_2= 0), I can't get any solution where z <> 0 or w <> 0.

@Carl Love Here's the same thing done in code that should work in Maple 2015:
 

Download IntEq.mw

@Carl Love Gimme a moment, and I'll retrofit that to your Maple 2015.

@LichengZhang The English word "next" as used by John May implies something in the future. Maple 2019.2's release is something in the past.

Are you saying that after 6 years on MaplePrimes, you don't know how to even enter the above equations into Maple?

@Kitonum Please post worksheets inline so that I can read them on my phone. 

Please post worksheets inline so that I can read them on my phone.

@dingtianlidi Hmm, I see that you're right. I couldn't do anything to get colorscheme= ["xyzcoloring", ...] to work with tubeplot. But it won't give an error message either! Unfortunately, that misled me to believe that my previous plot was correct.

Here's an alternative which I'm sure works (as can be seen in the plot below). We use the old-style option color= COLOR(HUE, C(t)) where C(t) is an expression in the parameter t scaled to 0..1.
 

Download ColoredTubeplot.mw

Note that x+y+z is constant 5 on the circle, so that doesn't make a good coloring function.

The radius option to tubeplot refers to the cross-sectional radius of the tube, not the radius of the overall circle.

@Carl Love Even without the wireframe, the use of cylindrical coordinates for the surface eliminates the gap between the upper and lower surfaces, even at modest resolution (I used 53x53 above).

There must be an underlying implementation of Maple supporting this Mobius. To what extent does the Mobius user have access to that? It would be easy to write a quaternion package for Maple. Would you be able to install and access it?

@zphaze I formally reported the bug.

It's not a new feature. Loops have always been that way. 

@ActiveUser All parts of Maple"s looping command that come before the word do are optional and always have been. 

@Scot Gould While it is true that the originally posted worksheet is missing a division operator in the parameters section of its Explore command, this is not the cause of the errors shown,. If you compare your worksheet with the OP's, you'll see that the latter has no boundary markers separating the regions of expository text from the executable code. (These markers can be seen in the extreme left margin of almost any worksheet.) I don't know whether this is the OP's doing, or whether the worksheet got mangled by MapleCloud.