-flux: Compute flux of fields through rectangular areas

In this section you may compute the flux of a field through a rectangular area.

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 # Flags: nomenu, noprompt, nomessage,                                        #
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 # section: -flux                                                             #
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 # symbol  = h_1                                                              #
 # quantity= h                                                                #
 # solution= 1                                                                #
 #                                                                            #
 # normal  = z                     -- [x|y|z]                                 #
 # cutat   = undefined             -- coordinate of the integration plane     #
 # xlow= undefined            , xhigh= undefined                              #
 # ylow= undefined            , yhigh= undefined                              #
 # zlow= undefined            , zhigh= undefined                              #
 #    ( used: @cutat : undefined )                                            #
 #    ( used: @xlow  : undefined        , @xhigh  : undefined )               #
 #    ( used: @ylow  : undefined        , @yhigh  : undefined )               #
 #    ( used: @zlow  : undefined        , @zhigh  : undefined )               #
 # @flux : undefined [undefined]                                              #
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 # doit, ?, return, end, help, ls                                             #
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• symbol= QUAN_ISOL:
  This is the full name of the symbol to be processed. This field has may be a 3D-E-field or a 3D-H-field.
• quantity= QUAN:
  This is the first part of the "symbol".
• solution= ISOL:
  This is the last part of the "symbol", the index of the "symbol".
• normal= [x|y|z]:
  The plane normal of the surface through which the flux integration shall be performed.
• cutat= :
  The "normal" coordinate of the area through which the integration shall be performed.
• xlow= ??, xhigh= ??, ylow= ??, yhigh= ??, zlow= ??, zhigh= ??:
  The coordinates of the rectangular area through which the flux integration shall be performed.
  If normal= x, the values xlow= ??, xhigh= ?? are ignored.
  If normal= y, the values ylow= ??, yhigh= ?? are ignored.
  If normal= z, the values zlow= ??, zhigh= ?? are ignored.
  The actually used values will be slightly different from the specified ones. After doit, the actually used values will be accessible as the symbolic variables @cutat, @xlow, @xhigh, @ylow, @yhigh, @zlow, @zhigh.
• doit:
  The flux integration is performed, the result is shown in the menu. The result is available as the symbol @flux for subsequent calculations.
  If the integrated field is an electric field, the result is
  
  $$@flux = \int \int \varepsilon_0 \varepsilon_r \vec{E} \cdot d\vec{F}$$
  
  
  If the integrated field is a magnetic field, the result is
  
  $$@flux = \int \int \mu _0 \mu _r \vec{H} \cdot d\vec{F}$$