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      <header alignment="Center" color="#a9a9a9">&amp;[DATE] &amp;[TIME] - &amp;[FILENAME]</header>
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      <text lang="eng">
        <p bold="true" fontName="Arial">Magic Maths</p>
      </text>
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    <region id="1" left="18" top="54" width="70" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
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        <p fontName="Arial">Formulae</p>
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          <e type="operand">W</e>
          <e type="function" args="1">f.1</e>
          <e type="operand">W</e>
          <e type="operand">w</e>
          <e type="operand">t</e>
          <e type="operator" args="2">+</e>
          <e type="bracket">(</e>
          <e type="operand">2</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">/</e>
          <e type="operand">W</e>
          <e type="operand">β</e>
          <e type="function" args="1">tan</e>
          <e type="operator" args="2">*</e>
          <e type="operand">l</e>
          <e type="operator" args="2">*</e>
          <e type="operand">w</e>
          <e type="operand">t</e>
          <e type="operator" args="2">*</e>
          <e type="operand">t</e>
          <e type="operand">2</e>
          <e type="operator" args="2">^</e>
          <e type="operand">3</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">+</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">+</e>
          <e type="operand">W</e>
          <e type="operand">α</e>
          <e type="function" args="1">tan</e>
          <e type="operator" args="2">*</e>
          <e type="operand">l</e>
          <e type="operator" args="2">*</e>
          <e type="operand">w</e>
          <e type="operand">t</e>
          <e type="operator" args="2">*</e>
          <e type="operand">w</e>
          <e type="operand">2</e>
          <e type="operator" args="2">^</e>
          <e type="operand">3</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">+</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">+</e>
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          <e type="operand">W</e>
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          <e type="operand">W</e>
          <e type="operand">β</e>
          <e type="function" args="1">tan</e>
          <e type="operator" args="2">*</e>
          <e type="operand">2</e>
          <e type="operand">w</e>
          <e type="operand">t</e>
          <e type="operator" args="2">+</e>
          <e type="bracket">(</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">:</e>
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    <region id="4" left="387" top="126" width="132" height="45" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">W</e>
          <e type="function" args="1">f.3</e>
          <e type="operand">W</e>
          <e type="operand">α</e>
          <e type="function" args="1">tan</e>
          <e type="operator" args="2">*</e>
          <e type="operand">2</e>
          <e type="operand">w</e>
          <e type="operand">t</e>
          <e type="operator" args="2">+</e>
          <e type="bracket">(</e>
          <e type="operator" args="2">*</e>
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          <e type="operator" args="2">:</e>
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      <text lang="eng">
        <p fontName="Arial">Overlord amazing solution</p>
      </text>
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      <math>
        <input>
          <e type="operand">P.W</e>
          <e type="operand">W</e>
          <e type="operand">f.max</e>
          <e type="operator" args="2">*</e>
          <e type="operand">W</e>
          <e type="function" args="1">f.1</e>
          <e type="bracket">(</e>
          <e type="operand">2</e>
          <e type="operator" args="2">^</e>
          <e type="operand">W</e>
          <e type="function" args="1">f.2</e>
          <e type="bracket">(</e>
          <e type="operand">2</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">+</e>
          <e type="operand">W</e>
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          <e type="bracket">(</e>
          <e type="operand">2</e>
          <e type="operator" args="2">^</e>
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      <text lang="eng">
        <p fontName="Arial">Notice that Overlord soltuion is independent of W</p>
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        <p fontName="Arial">Symbolic solution</p>
      </text>
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          <e type="operand">W</e>
          <e type="function" args="1">f.1</e>
          <e type="bracket">(</e>
          <e type="operand">2</e>
          <e type="operator" args="2">^</e>
          <e type="operand">W</e>
          <e type="function" args="1">f.2</e>
          <e type="bracket">(</e>
          <e type="operand">2</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">+</e>
          <e type="operand">W</e>
          <e type="function" args="1">f.3</e>
          <e type="bracket">(</e>
          <e type="operand">2</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">+</e>
          <e type="function" args="1">sqrt</e>
          <e type="operand">f.max</e>
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          <e type="operand">W</e>
          <e type="function" args="2">solve</e>
          <e type="function" args="1">maple</e>
          <e type="operand">1</e>
          <e type="function" args="2">el</e>
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        <p fontName="Arial">It's a really complicate expression</p>
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      <math>
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          <e type="operand">P.WS</e>
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          <e type="operand">w</e>
          <e type="operand">t</e>
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          <e type="bracket">(</e>
          <e type="operator" args="2">*</e>
          <e type="operand">t</e>
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          <e type="operand">w</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">+</e>
          <e type="bracket">(</e>
          <e type="operator" args="2">*</e>
          <e type="operand">w</e>
          <e type="operand">3</e>
          <e type="operand">t</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">+</e>
          <e type="bracket">(</e>
          <e type="operator" args="2">*</e>
          <e type="operand">w</e>
          <e type="operator" args="2">*</e>
          <e type="operand">f.max</e>
          <e type="operator" args="2">*</e>
          <e type="operand">t</e>
          <e type="operator" args="2">*</e>
          <e type="operand">t</e>
          <e type="operand">t</e>
          <e type="operand">t</e>
          <e type="operand">w</e>
          <e type="operand">w</e>
          <e type="operand">β</e>
          <e type="function" args="1">tan</e>
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          <e type="function" args="1">tan</e>
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          <e type="operand">59</e>
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          <e type="operand">30</e>
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          <e type="operand">9</e>
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          <e type="operand">2</e>
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          <e type="operand">59</e>
          <e type="operand">w</e>
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          <e type="operator" args="2">*</e>
          <e type="operand">2</e>
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          <e type="operator" args="2">*</e>
          <e type="operand">21</e>
          <e type="operand">β</e>
          <e type="function" args="1">tan</e>
          <e type="operator" args="2">*</e>
          <e type="operand">26</e>
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          <e type="function" args="1">tan</e>
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          <e type="bracket">(</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">+</e>
          <e type="bracket">(</e>
          <e type="operator" args="2">*</e>
          <e type="operand">6</e>
          <e type="operand">w</e>
          <e type="operand">5</e>
          <e type="operand">w</e>
          <e type="operator" args="2">*</e>
          <e type="operand">2</e>
          <e type="operand">l</e>
          <e type="operator" args="2">*</e>
          <e type="operand">26</e>
          <e type="operand">β</e>
          <e type="function" args="1">tan</e>
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          <e type="operand">21</e>
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          <e type="operator" args="2">+</e>
          <e type="bracket">(</e>
          <e type="operator" args="2">*</e>
          <e type="operand">12</e>
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          <e type="operand">2</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">*</e>
          <e type="operand">6</e>
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          <e type="function" args="1">tan</e>
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          <e type="function" args="1">tan</e>
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          <e type="operand">13</e>
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          <e type="operand">6</e>
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          <e type="operand">9</e>
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          <e type="operand">36</e>
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          <e type="bracket">(</e>
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          <e type="operand">1152</e>
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          <e type="operand">4</e>
          <e type="operand">l</e>
          <e type="operand">2</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">*</e>
          <e type="operand">2</e>
          <e type="operand">β</e>
          <e type="function" args="1">tan</e>
          <e type="operator" args="2">*</e>
          <e type="operand">16</e>
          <e type="operand">α</e>
          <e type="function" args="1">tan</e>
          <e type="operator" args="2">*</e>
          <e type="operand">11</e>
          <e type="operand">β</e>
          <e type="function" args="1">tan</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">+</e>
          <e type="bracket">(</e>
          <e type="operator" args="2">*</e>
          <e type="operand">9</e>
          <e type="operand">α</e>
          <e type="function" args="1">tan</e>
          <e type="operand">2</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">+</e>
          <e type="bracket">(</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">+</e>
          <e type="bracket">(</e>
          <e type="operator" args="2">*</e>
          <e type="operand">88</e>
          <e type="operand">w</e>
          <e type="operator" args="2">*</e>
          <e type="operand">β</e>
          <e type="function" args="1">tan</e>
          <e type="operator" args="2">*</e>
          <e type="operand">l</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">+</e>
          <e type="bracket">(</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">+</e>
          <e type="bracket">(</e>
          <e type="operator" args="2">*</e>
          <e type="operand">36</e>
          <e type="operand">w</e>
          <e type="operand">5</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">*</e>
          <e type="operand">β</e>
          <e type="function" args="1">tan</e>
          <e type="operator" args="2">*</e>
          <e type="operand">l</e>
          <e type="operator" args="2">*</e>
          <e type="operand">w</e>
          <e type="operand">2</e>
          <e type="operand">l</e>
          <e type="operator" args="2">*</e>
          <e type="operand">4</e>
          <e type="operand">β</e>
          <e type="function" args="1">tan</e>
          <e type="operator" args="2">*</e>
          <e type="operand">3</e>
          <e type="operand">α</e>
          <e type="function" args="1">tan</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">+</e>
          <e type="bracket">(</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">+</e>
          <e type="bracket">(</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">+</e>
          <e type="operand">216</e>
          <e type="operand">w</e>
          <e type="operator" args="2">*</e>
          <e type="operand">β</e>
          <e type="function" args="1">tan</e>
          <e type="operator" args="2">*</e>
          <e type="operand">l</e>
          <e type="operand">2</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">*</e>
          <e type="operand">t</e>
          <e type="operand">4</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">*</e>
          <e type="operand">α</e>
          <e type="function" args="1">tan</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">+</e>
          <e type="bracket">(</e>
          <e type="operator" args="2">*</e>
          <e type="operand">36</e>
          <e type="operand">β</e>
          <e type="function" args="1">tan</e>
          <e type="operand">2</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">*</e>
          <e type="operand">l</e>
          <e type="operand">2</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">*</e>
          <e type="operand">w</e>
          <e type="operand">6</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">+</e>
          <e type="function" args="1">sqrt</e>
          <e type="operator" args="2">/</e>
        </result>
      </math>
    </region>
    <region id="13" left="18" top="513" width="117" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
      <text lang="eng">
        <p fontName="Arial">It's the same!!!. Amazing</p>
      </text>
    </region>
    <region id="14" left="198" top="513" width="304" height="34" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">P.W</e>
          <e type="operand">P.WS</e>
          <e type="operator" args="2">-</e>
          <e type="operand">symbolic</e>
          <e type="function" args="2">simplify</e>
          <e type="function" args="1">maple</e>
        </input>
        <result action="symbolic">
          <e type="operand">0</e>
        </result>
      </math>
    </region>
    <region id="15" left="18" top="558" width="78" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
      <text lang="eng">
        <p fontName="Arial">Numerical values</p>
      </text>
    </region>
    <region id="16" left="198" top="558" width="80" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">α</e>
          <e type="operand">12</e>
          <e type="operand" style="unit">deg</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region id="17" left="315" top="558" width="72" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">β</e>
          <e type="operand">7</e>
          <e type="operand" style="unit">deg</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region id="18" left="531" top="558" width="119" height="41" color="#000000" bgColor="#ffffff" fontSize="10">
      <math optimize="2" decimalPlaces="1">
        <input>
          <e type="operand">f.max</e>
          <e type="operand">2182</e>
          <e type="operand" style="unit">lbf</e>
          <e type="operand" style="unit">in</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region id="19" left="198" top="585" width="88" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">t</e>
          <e type="operand">1.53</e>
          <e type="operand" style="unit">in</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region id="20" left="306" top="585" width="80" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">w</e>
          <e type="operand">4.2</e>
          <e type="operand" style="unit">in</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region id="21" left="414" top="585" width="88" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">l</e>
          <e type="operand">3.11</e>
          <e type="operand" style="unit">in</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region id="22" left="18" top="621" width="138" height="56" color="#000000" bgColor="#ffffff" fontSize="10">
      <text lang="eng">
        <p fontName="Arial">Numeric evaluation of the symbolic solution</p>
      </text>
    </region>
    <region id="23" left="198" top="621" width="150" height="30" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">P.WS</e>
        </input>
        <result action="numeric">
          <e type="operand">49737.0504</e>
          <e type="operand" style="unit">N</e>
          <e type="operator" args="2">*</e>
        </result>
      </math>
    </region>
    <region id="24" left="18" top="693" width="157" height="56" color="#000000" bgColor="#ffffff" fontSize="10">
      <text lang="eng">
        <p fontName="Arial">Usual and generic SMath implementation for the solver</p>
      </text>
    </region>
    <region id="25" left="198" top="693" width="44" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand" style="unit">u</e>
          <e type="operand" style="unit">N</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region id="26" left="306" top="693" width="109" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">W</e>
          <e type="function" args="1">Clear</e>
        </input>
        <result action="numeric">
          <e type="operand">1</e>
        </result>
      </math>
    </region>
    <region id="27" left="468" top="693" width="273" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
      <text lang="eng">
        <p fontName="Arial">Notice that actually W isn't defined yet!</p>
      </text>
    </region>
    <region id="28" left="198" top="738" width="308" height="43" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">eq</e>
          <e type="operand">W</e>
          <e type="function" args="1">f.1</e>
          <e type="bracket">(</e>
          <e type="operand">2</e>
          <e type="operator" args="2">^</e>
          <e type="operand">W</e>
          <e type="function" args="1">f.2</e>
          <e type="bracket">(</e>
          <e type="operand">2</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">+</e>
          <e type="operand">W</e>
          <e type="function" args="1">f.3</e>
          <e type="bracket">(</e>
          <e type="operand">2</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">+</e>
          <e type="function" args="1">sqrt</e>
          <e type="operand">f.max</e>
          <e type="operator" args="2">-</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region id="29" left="198" top="801" width="311" height="47" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">P.WN</e>
          <e type="operand" style="unit">u</e>
          <e type="operand">W</e>
          <e type="operand">W</e>
          <e type="operand" style="unit">u</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">:</e>
          <e type="operand">eq</e>
          <e type="operand">2</e>
          <e type="operand">1</e>
          <e type="function" args="4">line</e>
          <e type="operand">W</e>
          <e type="function" args="2">roots</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">:</e>
        </input>
        <result action="numeric">
          <e type="operand">49737.0504</e>
          <e type="operand" style="unit">N</e>
          <e type="operator" args="2">*</e>
        </result>
      </math>
    </region>
    <region id="30" left="585" top="801" width="131" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
      <text lang="eng">
        <p fontName="Arial">The same as the symbolic solution</p>
      </text>
    </region>
    <region id="31" left="18" top="855" width="147" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
      <text lang="eng">
        <p fontName="Arial">W isn't defined, this give an error ...</p>
      </text>
    </region>
    <region id="32" left="198" top="855" width="60" height="30" color="#000000" bgColor="#ffffff" fontSize="10">
      <math error="2">
        <input>
          <e type="operand">P.W</e>
        </input>
        <result action="numeric">
          <e type="operand">#</e>
        </result>
      </math>
    </region>
    <region id="33" left="18" top="900" width="138" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
      <text lang="eng">
        <p fontName="Arial">Just define any dummy W value ...</p>
      </text>
    </region>
    <region id="34" left="198" top="909" width="72" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">W</e>
          <e type="operand">6</e>
          <e type="operand" style="unit">kip</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region id="35" left="18" top="954" width="148" height="56" color="#000000" bgColor="#ffffff" fontSize="10">
      <text lang="eng">
        <p fontName="Arial">and see the miracle maths in the overlord solution</p>
      </text>
    </region>
    <region id="36" left="198" top="954" width="144" height="30" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">P.W</e>
        </input>
        <result action="numeric">
          <e type="operand">49737.0504</e>
          <e type="operand" style="unit">N</e>
          <e type="operator" args="2">*</e>
        </result>
      </math>
    </region>
    <region id="37" left="18" top="1026" width="58" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <input>
          <e type="operand">Alvaro</e>
        </input>
      </math>
    </region>
  </regions>
</worksheet>