Clear["Global`*"]
f[x_]:=Exp[-1/x^2]
{f[x],f'[x],f''[x]}

Clear["Global`*"]
f[n_]:=ConstantArray[1,{n+1,n+1}]+Table[Boole[i==j&&i!=1]*(i-2-x),{i,1,n+1},{j,1,n+1}]
Do[Print[Det[f[k]]],{k,3,7}]
Do[Print[Inverse[f[k]]//MatrixForm],{k,3,7}]

Clear["Global`*"]
f[x_List]:=Sum[Sum[Boole[x[[i]]>x[[j]]],{j,1,i}],{i,2,Length[x]}]
g[x_List]:=Sum[Sum[Boole[x[[i]]<x[[j]]],{j,1,i}],{i,2,Length[x]}]
{f[{1,3,6,9}],g[{1,3,6,9}]}

Clear["Global`*"]
f[n_]:=Graphics3D[{
Line[list=Table[RandomReal[{-1,1},3],{k,1,n}]],
Line[{list[[1]],list[[Length[list]]]}]
}]
f[10]

Clear["Global`*"]
list=RandomInteger[100,10]
arithmean[x_List]:=Total[x]/Length[x];
geomean[x_List]:= Product[x[[k]],{k,1,Length[x]}]^(1/Length[x])
harmean[x_List]:=Length[x]/Total[1/x]
{arithmean[list],geomean[list],harmean[list]}

Clear["Global`*"]
swaprow[matrix_,i_,j_]:=Module[{newmatrix},newmatrix=matrix;newmatrix[[{i,j}]]=matrix[[{j,i}]];newmatrix]
mulrow[matrix_,i_,x_]:=Module[{newmatrix},newmatrix=matrix;newmatrix[[i]]=newmatrix[[i]]*x;newmatrix]
subrow[matrix_,i_,j_,x_]:=Module[{newmatrix},newmatrix=matrix;newmatrix[[i]]-=newmatrix[[j]]*x;newmatrix]
m=RandomInteger[10,{3,3}];
{m//MatrixForm,swaprow[m,1,2]//MatrixForm,mulrow[m,1,2]//MatrixForm,subrow[m,1,2,3]//MatrixForm}

Clear["Global`*"]
g[x_]:=Piecewise[{{Log10[x],x>10},{Exp[x]+1,-10<=x<=10},{Abs[x],x<-10}}]
{g[15],g[5.2],g[-15]}

Clear["Global`*"]
x[t_]:=a*Cos[t]^3
y[t_]:=a*Sin[t]^3
Integrate[x[t]*y'[t]-y[t]*x'[t],{t,0,2*Pi}]/2