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  <settings>
    <identity>
      <id>3e7cde71-cba3-47f5-8c57-4bdcb0c65032</id>
      <revision>25</revision>
    </identity>
    <calculation>
      <precision>4</precision>
      <exponentialThreshold>5</exponentialThreshold>
      <fractions>decimal</fractions>
    </calculation>
    <pageModel active="true" printAreas="true" simpleEqualsOnly="false" printBackgroundImages="true">
      <paper id="9" orientation="Portrait" width="827" height="1169" />
      <margins left="39" right="39" top="39" bottom="39" />
      <header alignment="Center" color="#a9a9a9">&amp;[DATE] &amp;[TIME] - &amp;[FILENAME]</header>
      <footer alignment="Center" color="#a9a9a9">&amp;[PAGENUM] / &amp;[COUNT]</footer>
      <backgrounds />
    </pageModel>
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      <assembly name="Text Region" version="1.9.4909.6785" guid="485d28c5-349a-48b6-93be-12a35a1c1e39" />
      <assembly name="MaximaPlugin" version="1.0.5040.39716" guid="44011c1e-5d0d-4533-8e68-e32b5badce41" />
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  </settings>
  <region id="0" left="18" top="18" width="315" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p underline="true">int() asks for assumtions if required</p>
    </text>
  </region>
  <region id="1" left="18" top="45" width="279" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand" style="string">cleanup</e>
        <e type="function" preserve="true" args="1">MaximaControl</e>
      </input>
      <result action="symbolic">
        <e type="operand" style="string">done</e>
      </result>
    </math>
  </region>
  <region id="2" left="324" top="45" width="241" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>This resets the assume list.</p>
    </text>
  </region>
  <region id="3" left="18" top="81" width="625" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand" style="string">takeover</e>
        <e type="function" preserve="true" args="1">MaximaControl</e>
      </input>
      <result action="numeric">
        <e type="operand" style="string">int(), diff(), sum() and lim() now use Maxima</e>
      </result>
    </math>
  </region>
  <region id="4" left="18" top="117" width="619" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>Maxima cannot compute the integral without knowledge about the sign of x.0</p>
    </text>
  </region>
  <region id="5" left="18" top="153" width="108" height="51" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">x</e>
        <e type="function" args="1">ε</e>
        <e type="operand">ε.0</e>
        <e type="operand">x</e>
        <e type="operand">x.0</e>
        <e type="operator" args="2">/</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="6" left="135" top="153" width="120" height="60" color="#000000" bgColor="#ffffff" fontSize="10">
    <math optimize="2">
      <input>
        <e type="operand">x</e>
        <e type="function" args="1">y</e>
        <e type="operand">y.0</e>
        <e type="operand">x</e>
        <e type="operand">x.0</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="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="7" left="261" top="153" width="237" height="74" color="#000000" bgColor="#ffffff" fontSize="10">
    <math error="9">
      <input>
        <e type="operand">x</e>
        <e type="function" args="1">ε</e>
        <e type="operand">1</e>
        <e type="operand">x</e>
        <e type="function" args="1">y</e>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="2">diff</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" preserve="true" args="1">sqrt</e>
        <e type="operator" args="2">*</e>
        <e type="operand">x</e>
        <e type="operand">0</e>
        <e type="operand">x.0</e>
        <e type="function" preserve="true" args="4">int</e>
      </input>
      <result action="numeric">
        <e type="operand">#</e>
      </result>
    </math>
  </region>
  <region id="8" left="504" top="171" width="193" height="51" color="#000000" bgColor="#ffffff">
    <picture>
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  </region>
  <region id="9" left="18" top="243" width="235" height="36" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">x.0</e>
        <e type="operand">0</e>
        <e type="operator" args="2">&gt;</e>
        <e type="function" args="1">assume</e>
        <e type="function" preserve="true" args="1">Maxima</e>
      </input>
      <result action="symbolic">
        <e type="operand">x.0</e>
        <e type="operand">0</e>
        <e type="operator" args="2">&gt;</e>
      </result>
    </math>
  </region>
  <region id="10" left="261" top="243" width="417" height="105" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">x</e>
        <e type="function" args="1">ε</e>
        <e type="operand">1</e>
        <e type="operand">x</e>
        <e type="function" args="1">y</e>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="2">diff</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" preserve="true" args="1">sqrt</e>
        <e type="operator" args="2">*</e>
        <e type="operand">x</e>
        <e type="operand">0</e>
        <e type="operand">x.0</e>
        <e type="function" preserve="true" args="4">int</e>
      </input>
      <result action="symbolic">
        <e type="operand">ε.0</e>
        <e type="operand">4</e>
        <e type="operand">y.0</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">*</e>
        <e type="operand">x.0</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">+</e>
        <e type="bracket">(</e>
        <e type="operand">3</e>
        <e type="operand">2</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">^</e>
        <e type="operand">x.0</e>
        <e type="operand">3</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">12</e>
        <e type="operand">y.0</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">/</e>
      </result>
    </math>
  </region>
  <region id="11" left="18" top="351" width="347" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p underline="true">int() now treats units always as positive</p>
    </text>
  </region>
  <region id="12" left="18" top="387" width="710" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>Therefore, explicit sign assumptions are not required. This is a convenience feature.The units need not be defined.</p>
    </text>
  </region>
  <region id="13" left="18" top="423" width="279" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand" style="string">cleanup</e>
        <e type="function" preserve="true" args="1">MaximaControl</e>
      </input>
      <result action="symbolic">
        <e type="operand" style="string">done</e>
      </result>
    </math>
  </region>
  <region id="14" left="324" top="423" width="241" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>This resets the assume list.</p>
    </text>
  </region>
  <region id="15" left="27" top="459" width="63" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">x.0</e>
        <e type="operand" preserve="false" style="unit">x.0</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="16" left="108" top="459" width="63" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">y.0</e>
        <e type="operand" preserve="false" style="unit">y.0</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="17" left="27" top="468" width="420" height="105" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">x</e>
        <e type="function" args="1">ε</e>
        <e type="operand">1</e>
        <e type="operand">x</e>
        <e type="function" args="1">y</e>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="2">diff</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" preserve="true" args="1">sqrt</e>
        <e type="operator" args="2">*</e>
        <e type="operand">x</e>
        <e type="operand">0</e>
        <e type="operand">x.0</e>
        <e type="function" preserve="true" args="4">int</e>
      </input>
      <result action="symbolic">
        <e type="operand">ε.0</e>
        <e type="operand">4</e>
        <e type="operand" preserve="false" style="unit">y.0</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">*</e>
        <e type="operand" preserve="false" style="unit">x.0</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">+</e>
        <e type="bracket">(</e>
        <e type="operand">3</e>
        <e type="operand">2</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">^</e>
        <e type="operand" preserve="false" style="unit">x.0</e>
        <e type="operand">3</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">12</e>
        <e type="operand" preserve="false" style="unit">y.0</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">/</e>
      </result>
    </math>
  </region>
  <region id="18" left="18" top="576" width="267" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>This also works for ODE solving</p>
    </text>
  </region>
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    <math>
      <input>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="1">Clear</e>
      </input>
      <result action="numeric">
        <e type="operand">1</e>
      </result>
    </math>
  </region>
  <region id="20" left="18" top="621" width="724" height="62" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">m</e>
        <e type="operand">t</e>
        <e type="function" args="1">x</e>
        <e type="operand">t</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="3">diff</e>
        <e type="operator" args="2">*</e>
        <e type="operand" preserve="false" style="unit">k.0</e>
        <e type="operand">t</e>
        <e type="function" args="1">x</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
        <e type="operand">F</e>
        <e type="operator" args="2">≡</e>
        <e type="operand">t</e>
        <e type="function" args="1">x</e>
        <e type="operand">t</e>
        <e type="function" args="3">ode2</e>
        <e type="function" preserve="true" args="1">Maxima</e>
      </input>
      <result action="none">
        <e type="operand">t</e>
        <e type="function" args="1">x</e>
        <e type="operand">F</e>
        <e type="operand" preserve="false" style="unit">k.0</e>
        <e type="operator" args="2">/</e>
        <e type="operand">k1</e>
        <e type="operand" preserve="false" style="unit">k.0</e>
        <e type="function" preserve="true" args="1">sqrt</e>
        <e type="operand">t</e>
        <e type="operand">m</e>
        <e type="function" preserve="true" args="1">sqrt</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">*</e>
        <e type="function" preserve="true" args="1">sin</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
        <e type="operand">k2</e>
        <e type="operand" preserve="false" style="unit">k.0</e>
        <e type="function" preserve="true" args="1">sqrt</e>
        <e type="operand">t</e>
        <e type="operand">m</e>
        <e type="function" preserve="true" args="1">sqrt</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">*</e>
        <e type="function" preserve="true" args="1">cos</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
        <e type="operator" args="2">≡</e>
      </result>
    </math>
  </region>
  <region id="21" left="18" top="684" width="556" height="60" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand" style="string">%</e>
        <e type="function" args="1">rootscontract</e>
        <e type="function" preserve="true" args="1">Maxima</e>
      </input>
      <result action="none">
        <e type="operand">t</e>
        <e type="function" args="1">x</e>
        <e type="operand">F</e>
        <e type="operand" preserve="false" style="unit">k.0</e>
        <e type="operator" args="2">/</e>
        <e type="operand">k1</e>
        <e type="operand" preserve="false" style="unit">k.0</e>
        <e type="operand">m</e>
        <e type="operator" args="2">/</e>
        <e type="function" preserve="true" args="1">sqrt</e>
        <e type="operand">t</e>
        <e type="operator" args="2">*</e>
        <e type="function" preserve="true" args="1">sin</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
        <e type="operand">k2</e>
        <e type="operand" preserve="false" style="unit">k.0</e>
        <e type="operand">m</e>
        <e type="operator" args="2">/</e>
        <e type="function" preserve="true" args="1">sqrt</e>
        <e type="operand">t</e>
        <e type="operator" args="2">*</e>
        <e type="function" preserve="true" args="1">cos</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
        <e type="operator" args="2">≡</e>
      </result>
    </math>
  </region>
  <region id="22" left="18" top="756" width="574" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p underline="true">Relief of size limitation for expressions in the translation process </p>
    </text>
  </region>
  <region id="23" left="18" top="783" width="138" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math optimize="2">
      <input>
        <e type="operand">vx</e>
        <e type="operand">0</e>
        <e type="operand">10</e>
        <e type="operand">0.05</e>
        <e type="function" preserve="true" args="3">range</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="24" left="189" top="783" width="97" height="33" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">t.0</e>
        <e type="operand">0</e>
        <e type="function" preserve="true" args="1">time</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="25" left="333" top="783" width="139" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">vx</e>
        <e type="function" preserve="true" args="1">length</e>
      </input>
      <result action="numeric">
        <e type="operand">201</e>
      </result>
    </math>
  </region>
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