... and make them 2d pineapple and peppers! 

@nm For me, I appreciate the option to choose "what you see is what you get" or the classic mode. I equate the option of different styles to being more inclusive. Pedagogically, the 2D math mode helps getting folks started with Maple more quickly. But when I need more complex and long code, I switch to 1D typesetting.  However, this problem shouldn't occur regardless of the format.

@nm It appears to be a math mode issue:

@Carl Love The system is equivalent to long wires with constant current interacting with each other, but this person's example involves gravity. I've never read about such an example discovered in nature. But if you can link me to an example of long thin masses for which the dominate force is gravity, I'm happy to add that to my collection. 

If the idea is to mimic a magnetostatic force of the wires, then I suspect this is a unrealistic since the moving of the wires would affect the current in the wires. Upon reflection, this leads to a very cool computational (and realistic) question related to the retarding fields that I could add to a dynamics of electromagnetism course. Thanks!

@Carl Love Yep, that is correct. As for this problem, for the life of me I can't think of a physical justification for modeling gravity as a one over distance interaction.  I'm guessing this is simply a excercise in how to use dsolve with a more readable equation for the force.  When I ask the students to model it, I have them use the physically more accurate expression. 

@taro A good catch. However, in studing concepts in physics, extremum points come up frequently. From a physical perspective, these are two dimensional points: both the location and value of the function at the location are required. Neither of these Student[Calculus1] functions perform this task. Hence I return to the elegance of your original solution. ;-) Have a good day. 

@taro ..especially when your answer is so elegant and understandable. I wonder how often the Student[Calculus1] is used. 

with a minimal start up effort. Hence I use:
  1) Worksheet mode with
  2) 2D Input.

The combination helps keep students organized, but allows them to experience what-you-see-is-what-you-get. 

One can toggle between "2D Input" and "Maple Input". When in a Worksheet, with the cursor on a command line, i.e., where there is a ">" prompt, at the top of the document there is two buttons: "Text" and "Math". Note, this is below the drop down menus. The default is "Math" for the "2D Input."  Hit the "Text" button and now you are entering in "Maple Input." 

You can find more information in the help under: Entering Expressions In Maple Worksheets.

I hope that helps.

@Ronan ...but this style is is compromise between what Maple Help tends to promote, i.e., the Document format, and what the "old school / traditional programmers" tend to use, i.e., Worksheet with 1-D Maple Input. My sense with the students is that the intermediate version appears to have the most benefit for the least amount of potential misunderstandings. 

Interesting. I don't use this format for comments. I enter comments in the text blocks. Regardless, comments do appear to fail to copy only when one uses the "2D-Input" style. It does copy properly under "Maple Input". 

@taro 

While I love elegance and simplicity in the solution, I think they want to identify the extreme points of the expression, not the first derivative. 

A delightful post. I can immediately apply the 3rd, 4th and 5th techniques to some important simulation problems. Thumbs up.

@nm 

L:=[[1,2,3], [4, 5, 6]];
a:=array(1..nops(L));
seq(point(a[i], L[i]), i=1..nops(L));

then the labels are elements of an array: a[1], a[2] and not individual entities: a__||1, a__||2.

My apologies to this improperly constructed question. I correctly stated my goal, but in my haste to write the post, I created an obviously "nonsense" example. A more typical example I tend to solve is: x^2 – a = 0 where all constants are positive.

By my definition, slickest = fewest number of characters required, hence I like Tom Leslie’s answer the best.

So, while I probably didn’t deserve any “love” from this group, I do appreciate the fact that people thought critically, ignored the example, and provided solutions to the question. At this point, I am reminded of the famous quote by former U.S. Vice President and convicted felon Spiro T. Agnew, “Don’t judge us by what we say, judge us by what we do.”  

@Axel Vogt of using the evalf(Int()) process, it takes my verion of Maple (2016.1) 28 minutes to calculate. But, before I peformed the evalf() command, I did separate out the convert() function.

f(x) := exp(-(1/2)*x^2)/sqrt(2*Pi);
g := convert((f(x)*f(y)*x*x)*abs(x+y), piecewise, x);
gInt := Int(Int(g, x = -infinity .. infinity), y = -infinity .. infinity);
evalf(gInt);

However, if I ask it to determine the value(gInt), the calculation is within a second, as you pointed out. Hence I learned something about the difference between a numeric and an algebraic integration in Maple. 

(On a separate note: I'll bet the problem in the int() function is related to the bug someone found in the erf() function involving int() :  http://www.mapleprimes.com/posts/207471-Bug-In-Integrate.)