Replacement Rules

x=3+a

exp1->exp2

FullForm[%]

x/.a->5

ReplaceAll[3+a,a->5]

ReplaceAll[3+a,Rule[a,5]]

a^2-a+3/.a->5

x

x/.a->5

x

x=x/.a->5

x

x=3+a

3+a/.3->5

x/. 3->5

(3+x)/. 3->5

x

x/.a->x

6+a

Trace[x/.a->x]

x+y/.a->y

a/.{a->2,a->4}

a/.{a->2+b,b->4}

a//.{a->2+b,b->4}

a/.{{a->2},{a->4}}

{x,y}

x+y/.{a->y,y->4}

x+y//.{a->y,y->4}

3+y+a//.{a->y,y->a}

x+y//.{a->y,y->a}

{3+a+y,a+3+y,3+y+a}

x+y/.{a->y,y->a}
(x+y/.{a->y,y->a})/.{a->y,y->a}

x+y/.{a->y,y->2a}
(x+y/.{a->y,y->2a})/.{a->y,y->2a}
((x+y/.{a->y,y->2a})/.{a->y,y->2a})/.{a->y,y->2a}

{3 a,a^2,3^a,a^a,a!,Cos[a]}/.a->z

{3 a,a^2,3^a,a^a,a!,Cos[a]}/.a->4

{3 a,a^2,3^a,a^a,a!,Cos[a]}/.a->4.

{3 a,a^2,3^a,a^a,a!,Cos[a]}/.a^_->Infinity

{3 a,a^2,3^a,a^a,a!,Cos[a]}/._^_->Infinity

{3 a,a^2,3^a,a^a,a!,Cos[a]}/.a_^b_->b^a

difRules={dif[exp1_ exp2_]->exp1 dif[exp2]+dif[exp1] exp2,
dif[exp1_+exp2_]->dif[exp1]+dif[exp2]};

dif[a b c +b c]/.difRules

dif[a b c +b c]//.difRules

p[x_]:=x^5-7/3 x^4 + 13/12 x^3+7/12x^2-x/3

Plot[p[x],{x,-1,2}]

x/.NSolve[p'[x]==0,x]

Map[
Point[{#,p[#]}]&,
x/.NSolve[p'[x]==0,x]
]

Options[Plot]

Plot[p[x],{x,-1,2},
Epilog->{Pink,AbsolutePointSize[10],
Map[
Point[{#,p[#]}]&,
x/.NSolve[p'[x]==0,x]
]}
]

Options[ParametricPlot]

ParametricPlot[
{Sin[u]u,Cos[u]u},
{u,0,100}
]

ParametricPlot[
{Sin[u]u,Cos[u]u},
{u,0,100},
PlotPoints->125,
Axes->False,
MaxRecursion->0,
PlotStyle->Thick,
ColorFunction->(ColorData["Rainbow"][#3]&)
]

options[program]={plotpoints->100, option2->default2, option3->default3};

program[arg1_, arg2_,opts___]:=
(programDefinition/.opts)/.options[program]

inputL={-1,1,2,3,0,0,1,3,10,-8,1,2,3,-1,-2};

sub[{___,a_,m___,a_,___}]:=Length[{m}]

sub[inputL]

ReplaceAll, ReplaceRepeated

Map[Length,
ReplaceList[
inputL,
{___,a_,m___,a_,___}->{m}
]
]//ColumnForm

vs :=       -> vs :>

ReplaceList[
  inputL,
  {___, a_, m___, a_, ___} :> Length[{m}]
  ] // ColumnForm

list=RandomInteger[10,{30}]

ReplaceList[
list,
{___,a_,b_,___}/;Abs[a-b]==5->{a,b}
]

ReplaceList[
list,
{___,a_,b_,___}/;a==b+5||a==b-5->{a,b}
]

ReplaceList[
{1,2,3,4,5,6},
{x___,y__,z_}->{{x},{y},{z}}
]//ColumnForm

ReplaceList[
{1,2,3,4,5,6},
{x___,y___,z_}->{{x},{y},{z}}
]//ColumnForm

ReplaceList[
{1,2,3,4,5,6},
{x___,y__,z__}->{{x},{y},{z}}
]//Length

list=RandomInteger[5,{200}];

ReplaceList[
list,
{___,sub__,___}/;Apply[Plus,{sub}]==24->{sub}
]

Map[
{#,
Length[
ReplaceList[
list,
{___,sub__,___}/;Apply[Plus,{sub}]==#->{sub}
]
]
}&,
Range[10,360]
]//ListPlot

k=RandomReal[10,{6}]

Map [??,?]

{Sin[k[[1]] #]&, Sin[k[[2]] #]&, ...}

Binomial[6,2]