ParametricPlot3D[{2 Cos[t],2Sin[t],h},{t,0,2Pi},{h,0,3},ColorFunction ->ColorFunction[{x,y,z,t,h},(ColorData["GrayTones"][x^2/50])]]

ParametricPlot3D[{2Cos[t],2Sin[t],h},{t,0,2Pi},{h,0,3},ColorFunction ->Function[{x,y,z},Hue[Rescale[(z),{-4,4}]]]]

Plot3D[x^2-y^2,{x,-1,1},{y,-1,1}]

Plot3D[Abs[Sin[x+I y]],{x,-2 Pi,2 Pi},{y,-Pi/2,Pi/2},ColorFunction->Function[{x,y,z},Hue[Rescale[Arg[Sin[x+I y]],{-Pi,Pi}]]],ColorFunctionScaling->False,PlotStyle->Opacity[0.8],Mesh->False]

ParametricPlot3D[{E^s,t s,3s},{s,0,1},{t,0,1}]

ParametricPlot3D[{(1 + v/2 Cos[u/2])Cos[u],(1+v/2 Cos[u/2]) Sin[u],v/2 Sin[u/2]},{u,0,2 Pi},{v,-1,1}]

Show[
ParametricPlot3D[{2Cos[t],2Sin[t],z},{t,0,2 Pi},{z,0,2}],
VectorPlot3D[{x,0,0},{x,-2,2},{y,-2,2},{z,0,2}]
]

Show[
ParametricPlot3D[{2Cos[t],2Sin[t],z},{t,Pi,3Pi/2},{z,0,2}],
VectorPlot3D[{x,0,0},{x,-2,2},{y,-2,2},{z,0,2}]
]

Show[
ParametricPlot3D[{2Cos[t],y,2Sin[t]},{t,Pi,3Pi/2},{y,0,2}],
VectorPlot3D[{x,0,0},{x,-2,2},{y,0,2},{z,-2,2}]
]

Show[
ParametricPlot3D[{Cos[t] Sin[p],Sin[t]Sin[p],Cos[p]},{t,0,2Pi},{p,0,Pi}],
VectorPlot3D[#/Norm[#]^3&[{x,y,z}],{x,-2,2},{y,-2,2},{z,-1,1},VectorPoints->10,VectorScale->1,RegionFunction->(Norm[{#,#2,#3}]>.9&)]
]

Show[
ParametricPlot3D[{2s,s+t,1+s-t},{s,0,1},{t,0,1}],
VectorPlot3D[{x,y,0},{x,0,2},{y,0,2},{z,0,2}]
]

Show[
ParametricPlot3D[{ (1+((31 (z^2))/18)-((11 (z^3))/18))Cos[t], (1+((31 (z^2))/18)-((11 (z^3))/18)) Sin[t],2z},{t,0,2 Pi},{z,0,3}]
]

VectorPlot[{-y,x}/(x^2+y^2),{x,-3,3},{y,-3,3},VectorPoints->20,VectorScale->.2,RegionFunction->(Norm[{#,#2}]>.5&)]

VectorPlot3D[{-y,x,0}/(x^2+y^2),{x,-3,3},{y,-3,3},{z,0,5},VectorPoints->10,VectorScale->.1,RegionFunction->(Norm[{#,#2,#3}]>1&)]

ParametricPlot3D[{(1-t)Cos[s] + t (Cos[5s]+3)Cos[s],(1-t)Sin[s] + t(Cos[5s] +3)Sin[s],5t},{s,0,2Pi},{t,0,1}]

Show[
VectorPlot3D[{-y,x,0}/(x^2+y^2),{x,-3,3},{y,-3,3},{z,0,5},VectorPoints->10,VectorScale->.1,RegionFunction->(Norm[{#,#2,#3}]>1&)],
ParametricPlot3D[{(1-t)Cos[s] + t (Cos[5s]+3)Cos[s],(1-t)Sin[s] + t(Cos[5s] +3)Sin[s],5t},{s,0,2Pi},{t,0,1}]
]

N[((9+E^4)^(3/2) - (9+E^2)^(3/2)) Log[2]/3]