@John Fredsted 

getMinMax(53^3);

                                                3, 53

Should be   53, 53

See the thread with the same question  http://www.mapleprimes.com/questions/202504-Strange-Behavior-Of--Plotscontourplot

@gtbastos   Try:

restart;
M:=combinat:-permute([0$16,1$16],16):
S:=[seq(`if`(LinearAlgebra:-Modular:-Rank(3, Matrix(4,m, datatype= float[8]))>=3, m, NULL), m=M)]:  # The list of all such matrices, represented as the lists formed of the rows
nops(S);   # The total number of such matrices

@vv  For  x = 0.05 .. 2, y = 0 .. 2  the range of the function is bounded, but rather large. If we increase the lower bound for x-variable, then everything is OK even for the standard grid:

plots:-contourplot(1/(x^2+y^2), x = 0.5 .. 2, y = 0 .. 2, contours = 5, scaling = constrained);

@brian bovril 

seq(max(seq(add(d[s[i]]*x[s[i],s[i+1]], i=1..nops(s)-1) , s=t))<=K, t=Tour2);

d[1]*x[1, 2]+d[2]*x[2, 3]+d[3]*x[3, 4] <= K, max(d[1]*x[1, 2], d[1]*x[1, 3]+d[3]*x[3, 4]) <= K, max(d[1]*x[1, 3], d[1]*x[1, 2]+d[2]*x[2, 4]) <= K, max(d[1]*x[1, 4], d[1]*x[1, 2]+d[2]*x[2, 3]) <= K, max(d[1]*x[1, 2], d[1]*x[1, 3], d[1]*x[1, 4]) <= K

@Earl   Because a straight line intersects a circle at exactly one point if and only if it touches the circle at this point. Of course, for other curves this assertion may be false.

@mattyred99   I have no problems in Maple 2016, Maple 2015, Maple 16 and Maple 12. What version of Maple are you using?  Send a screenshot of your document with this error.

In Maple 2016:

Download Tangents.mw

@Fzen  This is called multiple assignment:

restart;
oldVars:=[a,b,c,d]: newVars:=[1,3,-9,5]:
assign(oldVars=~newVars);

a, b, c, d;
                                          1, 3, -9, 5

Addition. The  myfunc  procedure does the same thing:

myfunc:=proc(x)
local i;
for i from 1 to nops(oldVars) do
if x=oldVars[i] then return newVars[i] fi;
od;
undefined;
end proc:

oldVars:=[a,b,c,d]: newVars:=[1,3,-9,5]:
myfunc~(oldVars);  
                                            [1, 3, -9, 5]

@farjad_etg  It's strange. On my computer (Windows 10)  in Maple 2015.2 and 2016.2  everything works correctly 

The use  eval  and  ~  gives the simplest and shortest solution for the original problem:

sol:=solve([sin(t), 0 < t, t < 8*Pi], t, allsolutions, explicit);
eval~(t, [sol]);

You must provide the objective function so that everyone can try to work with it. And why  xx=0? Are you looking for a minimum of what function?

@mskalsi  I'm not an expert in pictures formats and therefore I cannot answer your question. For the forum, I always use the PNG format (or GIF for animations).

@Markiyan Hirnyk  I opened your file and saw these pictures:

@idol050279  I opened your file and saw the following picture:

For some reason, transparency  option does not work on your computer

@idol050279  I do not understand the reasons for your problems. The codes from your previous message work for me as expected. The code from your last file shows some of the points inside the cylinder, and some of the points  outside of the cylinder. I do not know what do you want. If you increase the diameter of the cylinder, then all the points will be inside it.