CellPrint[TextCell[Quiet[cdf =Manipulate[Column[{ "Usamos trapecio compuesto en conjunto con Romberg para aproxmar "<>integre(*<>"≈"TraditionalForm@formulas[[u]]*), Dynamic@SuFunc}],
Style[proposito,Bold,10],Spacer[{100,3}],
 (*Inicio contadores *)
 {{u,1,"Orden de la derivada para aproximar: "},2,2,2,ControlType->None},
{{ff,E^x,"f(x) = "},ControlType->InputField},
{{puntoA,2,"a = "},ControlType->InputField},
{{puntoB,10,"b = "},ControlType->InputField},
{{ene,4,"n = "},ControlType->InputField},
Button["Calcular", Dynamic@ SuFunc]
(* Fin contadores *)
,Alignment->Center,Deployed->True,AppearanceElements->"ResetButton",LocalizeVariables->True,ContinuousAction->False,FrameLabel->{{None,None},{Column[{,Row[{Style["Autores: Juan Félix Ávila Herrera y Enrique Vílchez Quesada",Bold,10,RGBColor[0,0,0.5]]}],Row[{Style["Escuela de Informática | Universidad Nacional de Costa Rica",Bold,10,RGBColor[0.5,0.1,0]]}]},Center],Style["Integración de Romberg", Bold,14, RGBColor[0,0.33,0.33]]}},
Initialization:>(
ClearAll["Global`*"];
integre = ToString[TraditionalForm@Defer[(∫_a^b)f[x]\[DifferentialD]x]];
escriba[lista_]:=Style[Row@lista,Black];
formulas ={nada,  (h/2)(f[a]+f[b]+2 (∑_(k=1)^(n-1))f[a+k*h]  )};
 
 
u=2;

(*($PreRead=(#/. s_String/;StringMatchQ[s,NumberString]&&Precision@ToExpression@s==MachinePrecision:>s<>"`12."&));*)
proposito ="Propósito: Usar integración de Romberg para aproximar "<>integre;
SuFunc := Module[{aux, resp, pt, coef},
resp[x_] := If[x==Round[x], x,ToString[x, InputForm]<> "≈"<>ToString[Sign[x]AccountingForm[Abs@N@x]]];

 f[t_] := ff/.x->t;
(**)
F[h_ ] :=  Module[{n=((b-a)/h)/.{a->puntoA, b->puntoB}},

 
(h/2)(f[a]+f[b]+2 (∑_(k=1)^(n-1))f[a+k*h]  )/.{a->puntoA, b->puntoB}
];
 
 
Q =Table[0, {i, ene}, {i, ene}];
For[j=1,j≤ene,j++,
For[i=1,i≤ene,i++, Q[[i, j]] = Which[j==1,F[((puntoB-puntoA)/(2^(i-1))) ] , j>i, 0,True,  (((4^(j-1))Q[[i, j-1]]-Q[[i-1, j-1]])/((4^(j-1))-1))]; 
]
];
Q =N[Q];
aux =Q[[ene, ene]];
(**)
aux =MatrixForm@Q; 
aux
];
Dynamic@SuFunc
)]],"Text"]]