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public text v1 · immutablefitfun[fun_, tofit_, params_, x_, range_] :=
Module[{steps = 11},
xvals = Range[range[[1]],
range[[2]], (range[[2]] - range[[1]])/steps];
yvals = fun[#] & /@ xvals;
sol = FindFit[Thread[{xvals, yvals}], tofit, params, x];
tofit /. sol]
fitfun[x, a Sqrt[x], {a}, x, {0, 1}]