I corected the placement of the restart and the other suggestions regarding variable timeT (thanks for the advice Tom however the suggestions really were not very applicable to a resolution, except for possibly the ill-placed restart). In any case I am on the hunt for a solution...
Essentially I am looking for a function with guaranteed zeros at t=0 and 90ish (f(t)=-t(t-90))... that is periodic between the zeros (f(t)=-t(t-90)(some trig function that doesn't cross the horizontal axis). The concept is a rollercoaster type question in mapleTA (height of the coaster versus time). One of the questions about the function is at what time(s) is the coaster 10 feet from the ground. The major issue I am having is that for certain random generations, mapleTA only recognizes one possible input value given a specific output (between 0 and max height) despite there obviously being at least two inputs that match the output (according to the graph).
a := MapleTA:-Builtin:-range(1800, 2300, 100):
b := (1/10)*MapleTA:-Builtin:-range(4, 8, 1):
timeT := MapleTA:-Builtin:-range(70, 100, 10):
f := -t*(b*t-b*timeT)^2*(cos(.15*t+4)^2-3)/a:
maxs := NLPSolve(f, t = 0 .. timeT, maximize):
maxim := maxs:
graph := plot(f, t = 0 .. timeT, gridlines = true, 0 .. maxim+10, labels = [t, h(t)], labeldirections = [horizontal, vertical]);
h_given := 10;
expr := h_given-f:
answer_t := Student:-Calculus1:-Roots(expr, t = 0 .. timeT);