Colouring stacked 2D in 3D

Question

Graphics3D[
 MapIndexed[
  Cases[#, Line[L_] :> {Red, 
      Line[Thread[{L[[All, 1]], #2[[1]]/5, L[[All, 2]]}]]}, -1] &, 
  Table[Plot[Sin[x]^n, {x, 0, \[Pi]}], {n, 5}]], Axes -> True, 
 BoxRatios -> {1, 1, 1}]

The above code generates an image shared below

However, I want each curve to be in a different colour, as in this (2D) PlotStyle -> ColorData[110, "ColorList"]

How do I do this in 3d? Please help me modify my above code to get the desired result in 3D

Answer 1

nc = 100;
nr = 5;
coords = Table[{x, n/nr, Sin[x]^n}, {n, nr}, {x, 0, π, π/nc}];

ListLinePlot3D[coords, PlotStyle -> 110, BoxRatios -> 1]

Answer 2

f[n_Integer, x_] := Sin[x]^n;
Graphics3D[
 MapIndexed[
  Cases[#, Line[L_] :> {Thick,ColorData[110][First[#2]], 
      Line[Thread[{L[[All, 1]], First[#2], L[[All, 2]]}]]}, -1] &, 
  Table[Plot[f[n, x], {x, 0, Pi}], {n, 5}]], Axes -> True, 
 BoxRatios -> {1, 1, 1}]