alternative box style: table and curve

Question

i see code in this forum and have a box "AAAA". now i want create box BBBB & CCCC with other style and same curve. BBBB box: add B1/B2/B3 box CCCC box: rotate "header" but don't rotate text Please see image and original code. Please help this code: Thanks

\documentclass[a4paper]{book}
\usepackage{amsmath,amssymb}%      pour les maths
\usepackage{enumitem}
\usepackage{wrapfig}
\usepackage{graphicx}
\usepackage{MnSymbol,wasysym}
\usepackage[svgnames]{xcolor}
\usepackage[most]{tcolorbox}
\usepackage{framed}
\usepackage{tikz}
\usepackage[utf8]{inputenc}
\usepackage[utf8]{vietnam}
%\usepackage[utf8]{english}
\usepackage[english]{babel}
\usepackage[format=plain,
            labelfont={bf,it},
            textfont=it]{caption}

%\newcommand\captionof[2]{\def\@captype{#1}\caption}

\usepackage{tikzsymbols} 
\newtcbtheorem{myLemma}{Long text here without counter }{lemmastyle}{thm}

\usetikzlibrary{calc, fit, backgrounds}
\usepackage{varwidth}

\newcommand{\mybox}[4][\textwidth-\pgfkeysvalueof{/pgf/inner xsep}-2mm]{%

\centering
\begin{tikzpicture}
\node[line width=0.5mm, inner ysep=10pt, text width=#1, outer sep=0] (text) {\begin{varwidth}{\textwidth}#4\end{varwidth}};
\node[text=white, above right, align=left] (title) at (text.north west) {#3};
\node[fit=(title) (text), line width=0.5mm, rounded corners, draw=#2, inner sep=0pt] (box){};
\begin{scope}[on background layer]
\fill[#2] (title.south west) -- (title.south east) to[out=0, in=180] ([xshift=1.5cm]title.east) -- (title.east-|box.north east) [rounded corners] -- (box.north east) -- (box.north west) [sharp corners] -- cycle;
\end{scope}
\end{tikzpicture} 
}

\newcommand{\myboxa}[4][\textwidth-\pgfkeysvalueof{/pgf/inner xsep}-2mm]{%

\centering
\begin{tikzpicture}
\node[line width=0.5mm, inner ysep=10pt, text width=#1, outer sep=0] (text) {\begin{varwidth}{\textwidth}#4\end{varwidth}};
\node[text=white, above right, align=left] (title) at (text.west north) {#3};
\node[fit=(title) (text), line width=0.5mm, rounded corners, draw=#2, inner sep=0pt] (box){};
\begin{scope}[on background layer]
\fill[#2] (title.west south) -- (title.west south) to[out=0, in=180] ([xshift=1.5cm]title.east) -- (title.east-|box.east north) [rounded corners] -- (box.east north) -- (box.west north) [sharp corners] -- cycle;
\end{scope}
\end{tikzpicture} 
}
\usepackage{pifont}

\begin{document}

\tcbset{sidebyside,
  size=minimal,
  colback=white,
  lower separated=false,
  halign upper=flush center,
  halign lower=flush left,
  lefthand width=2.5cm, 
  frame empty,
}


\mybox[10cm]{green!70!black}{AAAA }{
\begin{enumerate}
\item ....................................................\hspace*{1cm}..........................

\item ....................................................\hspace*{1cm}..........................

\end{enumerate}

}
\end{document}

Answer 1

This is a possible solution. It's based on my own answer code to Inspired beautiful box from Indesign which uses tcolorbox for these boxes design. With this solution it's easy to define a tcboxedraster or tcboxeditemize to include three boxes inside another one.

\documentclass[a4paper]{article}
\usepackage{amsmath,amssymb}
\usepackage{lmodern}
\usepackage[most]{tcolorbox}
\usepackage{lipsum}

\makeatletter
\tcbset{
    myhbox/.style 2 args={%
        enhanced, 
        breakable,
        colback=white,
        colframe=blue!30!black,
        attach boxed title to top left={yshift*=-\tcboxedtitleheight}, 
        title={#2},
        boxed title size=title,
        boxed title style={%
            sharp corners, 
            rounded corners=northwest, 
            colback=tcbcolframe, 
            boxrule=0pt,
        },
        underlay boxed title={%
            \path[fill=tcbcolframe] (title.south west)--(title.south east) 
                to[out=0, in=180] ([xshift=5mm]title.east)--
                (title.center-|frame.east)
                [rounded corners=\kvtcb@arc] |- 
                (frame.north) -| cycle; 
        },
        #1
    },
    myvbox/.style 2 args={%
        enhanced, 
        colback=white,
        colframe=blue!30!black,
        left=8mm,
        overlay={
            \node[rotate=90, anchor=north west, inner sep=2mm, text=white] (title@aux) at (frame.south west) {#2};
            \path[fill=tcbcolframe] (title@aux.south west)--(title@aux.south east) 
                to[out=90, in=270] ([yshift=5mm]title@aux.east)--
                (title@aux.center|-frame.north)
                [rounded corners=\kvtcb@arc] -| 
                (frame.west) |- (title@aux.west)[sharp corners] -- cycle;   
            \node[rotate=90, inner sep=2mm, text=white] at (title@aux) {#2};
        },
        #1
    },  
}   
\makeatother

\newtcolorbox{myhbox}[2][]{%
    myhbox={#1}{#2}
}

\newtcolorbox{myvbox}[2][]{%
    myvbox={#1}{#2}
}

\begin{document}

\begin{myhbox}{Long fancy title}
\begin{enumerate}
\item Show that 
\[D_2f(x,y) = \frac{\partial{}}{\partial{y}} \left ( \int_0^xg_1 (t,0)\ dt + \int_0^y g_2(x,s)\ ds \right)\]
\item Prove that 
\[\left(\forall x\in\mathbb{R}  \right)\left(\forall y \in \mathbb{R} \right) x\neq y\, \text{and} \, x+y \neq 2 \implies x^{2}-2x \neq y^2-2y\] 
\end{enumerate}
\end{myhbox}

\begin{myvbox}[colframe=red!80!black]{Long fancy title}
\begin{enumerate}
\item Show that 
\[D_2f(x,y) = \frac{\partial{}}{\partial{y}} \left ( \int_0^xg_1 (t,0)\ dt + \int_0^y g_2(x,s)\ ds \right)\]
\item Prove that 
\[\left(\forall x\in\mathbb{R}  \right)\left(\forall y \in \mathbb{R} \right) x\neq y\, \text{and} \, x+y \neq 2 \implies x^{2}-2x \neq y^2-2y\] 
\end{enumerate}
\end{myvbox}

\begin{tcboxeditemize}[raster columns=3, myhbox={colback=yellow!10, colframe=red!70!black}{Box \# \thetcbrasternum} ]{myhbox={colback=red!10}{External box}}
\tcbitem A
\tcbitem[notitle, myvbox={colback=green!70!black, height=4cm}{Box \# \thetcbrasternum}] B
\tcbitem C
\end{tcboxeditemize}

\end{document}

Note Previous code has been updated for compatibility with tcolorbox v4.20. If you're using previous versions, rename colors with form tcbcol... to older form tcbcol@....