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      <header alignment="Center" color="#a9a9a9">&amp;[DATE] &amp;[TIME] - &amp;[FILENAME]</header>
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    <math>
      <description active="true" position="Right" lang="eng">
        <p>Circle</p>
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        <p>Derivative</p>
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        <p>Symbolic </p>
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      <title lang="eng">
        <p>     Hatch [Martin]     </p>
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      <math>
        <description active="true" position="Top" lang="ger">
          <p>Erzeugt eine Matrix für die Darstellung vertikaler Linien zwischen den Funktionen f(x) und g(x) im Bereich von x1 bis x2 mit 2*n Linien.</p>
        </description>
        <description active="true" position="Top" lang="eng">
          <p>Generates a matrix for 2*N vertical lines (hatching) between functions f(x) and g(x) in x-range from x1 to x2</p>
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          <e type="operand">x.2</e>
          <e type="operand">x.1</e>
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          <e type="operand">N</e>
          <e type="operator" args="2">/</e>
          <e type="bracket">(</e>
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          <e type="operand">h</e>
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          <e type="operand">x.1</e>
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          <e type="operand">x.1</e>
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          <e type="operand">2</e>
          <e type="operand">2</e>
          <e type="function" preserve="true" args="6">mat</e>
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          <e type="operand">x</e>
          <e type="operand">x.1</e>
          <e type="operand">x.2</e>
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          <e type="operand">x.1</e>
          <e type="operand">dx</e>
          <e type="operator" args="2">+</e>
          <e type="function" preserve="true" args="3">range</e>
          <e type="operand">h</e>
          <e type="operand">h</e>
          <e type="operand">x</e>
          <e type="operand">dx</e>
          <e type="operand">2</e>
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          <e type="operand">x</e>
          <e type="operand">dx</e>
          <e type="operand">2</e>
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          <e type="function" args="1">g</e>
          <e type="operand">x</e>
          <e type="operand">dx</e>
          <e type="operand">2</e>
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          <e type="function" args="1">f</e>
          <e type="operand">x</e>
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          <e type="operand">x</e>
          <e type="operand">dx</e>
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          <e type="function" args="1">f</e>
          <e type="operand">x</e>
          <e type="operand">dx</e>
          <e type="operator" args="2">+</e>
          <e type="operand">x</e>
          <e type="operand">dx</e>
          <e type="operator" args="2">+</e>
          <e type="function" args="1">g</e>
          <e type="operand">4</e>
          <e type="operand">2</e>
          <e type="function" preserve="true" args="10">mat</e>
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          <e type="function" preserve="true" args="3">for</e>
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          <e type="operand">4</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="6">line</e>
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        <e type="operand">x</e>
        <e type="operand">1</e>
        <e type="operand">x</e>
        <e type="operand">2</e>
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    <math>
      <description active="true" position="Right" lang="eng">
        <p>Constrain the plot</p>
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        <e type="operand">x</e>
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        <e type="operand">x</e>
        <e type="function" args="1">g</e>
        <e type="operand">1</e>
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      <input>
        <e type="operand">x</e>
        <e type="function" args="1">Arc</e>
        <e type="operand">x</e>
        <e type="function" args="1">f</e>
        <e type="operand">x</e>
        <e type="function" args="2">int</e>
        <e type="function" preserve="true" args="1">maple</e>
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        <e type="operand">1</e>
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        <e type="operand">2</e>
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        <e type="operand">1</e>
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        <e type="operand">x</e>
        <e type="operand">2</e>
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    <plot type="2d" render="lines" scale_x="6.72749994932561" scale_y="21.1137767453526" scale_z="142.042931984432" rotate_x="0" rotate_y="0" rotate_z="0" transpose_x="-89" transpose_y="-111" transpose_z="0">
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        <e type="operand">x</e>
        <e type="function" args="1">f</e>
        <e type="operand">x</e>
        <e type="function" args="1">c</e>
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        <e type="operand">x</e>
        <e type="function" args="1">g</e>
        <e type="operand">x</e>
        <e type="function" args="1">f</e>
        <e type="operand">x</e>
        <e type="function" args="1">g</e>
        <e type="operand">0</e>
        <e type="operand">0.95</e>
        <e type="operand">20</e>
        <e type="function" args="5">hatch</e>
        <e type="operand">3</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="5">sys</e>
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    <plot type="2d" render="lines" scale_x="3.4522712143931" scale_y="9.46161390794744" scale_z="32.6640573361084" rotate_x="0" rotate_y="0" rotate_z="0" transpose_x="-1" transpose_y="50" transpose_z="0">
      <input>
        <e type="operand">x</e>
        <e type="function" args="1">Arc</e>
        <e type="operand">π</e>
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        <e type="operand">2</e>
        <e type="operator" args="2">/</e>
        <e type="operand">π</e>
        <e type="operator" args="1">-</e>
        <e type="operand">3</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="5">sys</e>
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    </plot>
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    <math evaluate="false">
      <description active="true" position="Top" lang="eng">
        <p>Smath integrator is Simpson.It does not have ∞ limit.No integrator will approach π.</p>
      </description>
      <input>
        <e type="operand">1</e>
        <e type="operand">x</e>
        <e type="operand">1</e>
        <e type="operand">x</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">-</e>
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        <e type="bracket">(</e>
        <e type="operand">2</e>
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        <e type="operand">x</e>
        <e type="operand">0</e>
        <e type="operand">0.999</e>
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        <e type="operand">#</e>
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      <description active="true" position="Top" lang="eng">
        <p>Simon Plouffe π  'n' incremental algorithm</p>
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        <e type="operand">1</e>
        <e type="operand">16</e>
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        <e type="operand">4</e>
        <e type="operand">8</e>
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        <e type="operand">1</e>
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        <e type="operand">8</e>
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        <e type="operand">4</e>
        <e type="operator" args="2">+</e>
        <e type="operator" args="2">/</e>
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        <e type="operand">1</e>
        <e type="operand">8</e>
        <e type="operand">k</e>
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        <e type="operand">5</e>
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        <e type="operator" args="2">/</e>
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        <e type="operand">1</e>
        <e type="operand">8</e>
        <e type="operand">k</e>
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        <e type="operand">6</e>
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        <e type="bracket">(</e>
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        <e type="bracket">(</e>
        <e type="operand">k</e>
        <e type="operand">0</e>
        <e type="operand">n</e>
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        <e type="operator" args="2">:</e>
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    </math>
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    <math fractionType="auto" decimalPlaces="15">
      <input>
        <e type="operand">13</e>
        <e type="function" args="1">pi</e>
      </input>
      <result action="numeric">
        <e type="operand">3.14159265358979</e>
      </result>
    </math>
  </region>
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    <math optimize="2" fractionType="auto" decimalPlaces="15">
      <input>
        <e type="operand">π</e>
        <e type="operand">3.14159265358979</e>
        <e type="operator" args="2">≡</e>
      </input>
    </math>
  </region>
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