@Markiyan Hirnyk  I often visit this site  http://www.mathforum.ru/forum/list/1/

Your expression can be greatly simplified if you reduce the fraction by  sqrt(s+thetac)  because

         A1*Dc*alpha1*s^2+A1*Dc*alpha1*s*thetac=A1*Dc*alpha1*s*(s+thetac)

@MrMarc  If you need a single solution, then you need to impose an additional condition. For example, the condition  x=y  leads to the unique solution:

solve({x+y = 373320, z = (x+y) / 0.44 - y -  y* (1 - 0.99), x=y});

         {x = 186660., y = 186660., z = 659927.9456}
 

 rlopez Many thanks for the detailed analysis of the code in  IntOverDomain  procedure and the great work you have done for this.

@acer  This is the perfection of skill!

@mohkam7 

restart;
MakeColored:=(s,c)->Typesetting:-mo(convert(s,string), mathcolor = c):

MakeColored(`ϵ`, "Green");
MakeColored(x, "Red")[MakeColored(i, "Red")];

@Markiyan Hirnyk  So what?

@Markiyan Hirnyk  My answer is just an alternative solution to the problem (without Statistics package). It remains to round 4.98 .. to the nearest integer. To be more pedantic, it is necessary to compare the values of the sums for n=4 and n=5 and choose the one that is closer to 0.95:

lambda:=2.6:
sum(lambda^k*exp(-lambda)/k!, k=0..4);
sum(lambda^k*exp(-lambda)/k!, k=0..5);

                          0.8774234888
                          0.9509628480
 

@idol050279  You have already received so many different tips and examples that it's time you made something yourself. Give your attempts to resolve and clearly indicate what exactly is causing you difficulties.

@rlopez  I think for the beginner your method is the simplest and most understandable solution to the problem. When I wrote about two ways, I just forgot about this method. So we already have 3 ways.

@Markiyan Hirnyk  You did not answer my question (...to display successive frames of animation). On the animation bar (if you use  plots:-animate  command) there is a special button that allows you to do this.

@Markiyan Hirnyk  How do you expect to display successive frames of animation with a specific step in this case?

@Rouben Rostamian   min(a,b) = (a + b - abs(a - b))/2

@one man  Try in the procedure to replace  r:=sqrt(add(d^~2))  with  r:=sqrt(`+`((d^~2)[ ]))  or  r:=sqrt(add(d[i]^2, i=1..nops(d))) .  Do not forget to restart first.

@Harry Garst  Here are three simple examples that confirm your observation:

Expr1:=a/(a+b+c);
algsubs(a+b+c=d, Expr1);

Expr2:=b/(a+b+c);
algsubs(a+b+c=d, Expr2);

Expr3:=c/(a+b+c);
algsubs(a+b+c=d, Expr3);

We see that the result depends on the position:  a  is the first in  a+b+c