I am new to Maple and need assistance optomizing the following function F with respect to t:

F := int(f, [yip = -infinity .. infinity, xip = -infinity .. infinity, tp = 0 .. t])

Where: f := exp(-(xip^2+yip^2)*(1/2))*exp(-((2*Pe*tp+x-xip)^2+(y-yip)^2+z^2)/(4*(t-tp)))/((4*Pi^(3/2))*(t-tp)^(3/2))

and

Pe := 10; x := 0; y := 8/10; z := 1/18

I have a plot of F from 0 to approximately 1/2 and I know what the shape of the function is:

Is is clear that there definitely is a maximum within this range of t (i.e. t=0 to 1/2). When I right click on the function F and click the "Optomization" tab, then "Maximize (local)" maple results in the following pink text "Error, (in Optimization:-NLPSolve) integration range or variable must be specified in the second argument, got HFloat(1.0) = 0 .. HFloat(1.0)"

Any help fixing the error and optimizing the function F will be appreciated. Thank you!

I am new to Maple. I am trying to numerically evaluate the following function with respect to the 3 variables "xop", "yop", and "tp". All other variables appearing in the function f are known (i.e. "x", "y", "z", "Pe", also "Pi" is the constant 3.1415...). "f" is shown below:

f := exp(-1/2*(xop^2+yop^2))*exp(-((x-xop-2*Pe*(t-tp))^2+(y-yop)^2+z^2)/(4*(t-tp)))/((4*Pi^(3/2))*(t-tp)^(3/2))

I am then defining "deltaT" as equal to the triple integral below:

deltaT := int(f, [yop = -(-xop^2+1)^(1/2) .. (-xop^2+1)^(1/2), xop = -1 .. 1, tp = 0 .. t])

When I try to evaluate this, Maple spits out an incredibly long answer full of variables and error functions:

deltaT := -0.7957747155e-1*(int(sqrt(5.-1.*tp)*(int(exp((0.5000000000e-2*(-200.*tp^2*xop^2+40000.*tp^3-4000.*tp^2*xop+2200.*tp*xop^2-617200.*tp^2+41860.*tp*xop-6050.*xop^2+3.170694*10^6*tp-109230.*xop-5.423499*10^6))/((-11.+2.*tp)*(-5.+tp)))*(erf((.1000000000*(10.*sqrt(-1.*xop^2+1.)*tp-55.*sqrt(-1.*xop^2+1.)-3.))/(sqrt(11.-2.*tp)*sqrt(5.-1.*tp)))+erf((.1000000000*(10.*sqrt(-1.*xop^2+1.)*tp-55.*sqrt(-1.*xop^2+1.)+3.))/(sqrt(11.-2.*tp)*sqrt(5.-1.*tp)))), xop = -1 .. 1))/((5-tp)^(3/2)*sqrt(11.-2.*tp)), tp = 0 .. 5))

Any help on figuring out why it is unable to numerically evaluate would be appriciated!

Thanks.