@Carl Love 

@Carl Love thx for your efforts. 

i tried to use the above code to model 3 dancers, 4 m apart. the ode plot didnt and the arc length might be wrong. could you fix it pls.

triangle_persuit.mw

@Carl Love and Kitonum for your solutions.

thanks also to ThomasRichard and @Carl Love for supportive comments regarding my questions on mapleprimes.

@tomleslie i concur with you. It doesn't seem in the "spirit" of the problem to do it like he did. He made a right angle cut to the small cheese OD, withdrew the knife and then another hemispherical cut. Then withdrew the knife and made another cut ( that's 3 cuts, not 1).

@tomleslie your solution got me thinking of an alternative way. I don't remember aall of those geometry formulas, but with integration, I only need to know the equation of a circle.

x^2+y^2=(16/2)^2;
yeq:=solve(%,y)[1];
#total area:
2*int(yeq,x=-8..8)=Pi*(16^2)/4;
#checks. Let D be the coordinate the cut has to make to remove 14Pi from the medium cheese.
2*int(yeq,x=D..8)=14*Pi;
fsolve(%);
#make the cut at coordinate of D [3.6671,0]
area of segment check:
2*int(yeq,x=%..8)=evalf(14*Pi);

BUT the solution on "School of Hard Sums", which doesn't require any fancy pants geomery or calculus, is found by placing the small cheese in the centre of the medium cheese and cutting a semicircular arc around it.
This C section is put with the small cheese=1 portion.

#Area of an annulus + area small cheese:
Pi*1/4*((16^2-12^2)/2+12^2);
50 Pi

@Thomas Richard 

Windows was indeed treating it as a text file. I removed the extension and success! Thx for your help.

I'm running win 7 BTW

@Thomas Richard thx for your input.

i removed the ini's from Maple18/win.bin, lib and Users.

i changed my text file to this:

interface(prompt=""):
e:=exp(1);
Digits:=15;
print("maple init loaded...");

And placed in  C:\Users\<my_account_mame>

Rebooted Maple and no result.

tried putting it into Maple18/win.bin, lib and Users (one at a time) -> same same

@tomleslie thx Tom.

Sorry i was not more succinct. I meant DirectSearch package.

I did state i was using M18.

You gave me the clue, I did a search on the MP website for " hdb" and saw what i'd known i'd seen b4, 

http://www.mapleprimes.com/posts/200289-Convert-Help-Of-Older-Maple-Version-To-18

@Carl Love it's a pity Maple doesn't have a Mathematica-esq "scan for issues" command.

@tomleslie and Kitonum. so logical.

Unfrortunately, Tom , when I run your code I get "Error, invalid input, expects 2 arguments, but received 1" .

in Maple 18....

@Carl Love thanks

@bfathi .sav are file extensions used by SPSS aern't they?

@Axel Vogt 

the orig expression consists of two gaussians and a decay function:

T1:=(1/2)*exp(-(1/2)*(X[4]-933)^2/63^2)*exp(-(1/2)*(X[2]-805)^2/55^2)/((1+exp((1/50)*X[4]-(1/50)*X[2]))*Pi*63*55);

On the subject of maximums, fsolve({diff(ln(T1), X[2]) = 0, diff(ln(T1), X[4]) = 0}); yields 

evalf(eval(T1, {X[2] = 845.348137692692, X[4]= 880.060572171785]}));

0.00000821.....

BUT best results with:

evalf(eval(T1, {X[2] = 843.611792749488, X[4] = 882.338775066865}));

0.00000819.....

I dont really follow your "fsolve locates it in..x=844.09".methodology. c(x) is one gaussian, f(x) is what? 1/(1+exp(x/50))?

@Markiyan Hirnyk 

@acer don't know why the fsolve didnt work.. im using an older version than you...v18.00, win7, 64 bit