﻿<?xml version="1.0" encoding="utf-8" standalone="yes"?>
<?application progid="SMath Studio Desktop" version="0.98.6179.21440"?>
<regions>
  <settings>
    <identity>
      <id>bcebf472-ab09-4d9f-9dea-f114746ebe04</id>
      <revision>9</revision>
    </identity>
    <calculation>
      <precision>15</precision>
      <exponentialThreshold>12</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>
    <dependencies>
      <assembly name="SMath Studio Desktop" version="0.98.6179.21440" guid="a37cba83-b69c-4c71-9992-55ff666763bd" />
      <assembly name="Math Region" version="0.98.6179.21440" guid="02f1ab51-215b-466e-a74d-5d8b1cf85e8d" />
      <assembly name="Custom Functions" version="1.1.6281.4594" guid="18dadffd-79a3-4cf9-aee1-d66deb0ea720" />
      <assembly name="Special Functions" version="1.11.6179.21442" guid="2814e667-4e12-48b1-8d51-194e480eabc5" />
      <assembly name="Maple Wrapper" version="1.0.6328.1700" guid="32dfd679-8cfd-483a-b79a-19d5ea838750" />
      <assembly name="Text Region" version="1.10.6179.21446" guid="485d28c5-349a-48b6-93be-12a35a1c1e39" />
      <assembly name="Plot Region" version="1.9.6179.21450" guid="c451c2b5-798b-4f08-b9ec-b90963d1ddaa" />
    </dependencies>
    <mode debug="true" />
  </settings>
  <region id="0" left="90" top="27" width="159" height="24" color="#0000ff" bgColor="#000000" fontSize="10">
    <math exponentialThreshold="5">
      <input>
        <e type="operand">ε</e>
        <e type="operand">1.5213508465462</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="1" left="81" top="72" width="164" height="45" color="#0000ff" bgColor="#000000" fontSize="10">
    <math decimalPlaces="4" exponentialThreshold="5">
      <input>
        <e type="operand">ζ</e>
        <e type="function" args="1">φ</e>
        <e type="operand">1</e>
        <e type="operand">ζ</e>
        <e type="operand">ε</e>
        <e type="function" preserve="true" args="1">cos</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">/</e>
        <e type="function" preserve="true" args="1">atan</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="2" left="387" top="90" width="189" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">1</e>
        <e type="function" args="1">φ</e>
      </input>
      <result action="numeric">
        <e type="operand">1.5214111794913</e>
      </result>
    </math>
  </region>
  <region id="3" left="81" top="126" width="240" height="158" color="#000000" bgColor="#ffffff" fontSize="10">
    <plot type="2d" render="lines" scale_x="1" scale_y="9.53793665091283" scale_z="9.53793665091283" rotate_x="0" rotate_y="0" rotate_z="0" transpose_x="0" transpose_y="0" transpose_z="0">
      <input>
        <e type="operand">x</e>
        <e type="function" args="1">φ</e>
      </input>
    </plot>
  </region>
  <region id="4" left="72" top="369" width="268" height="69" color="#0000ff" bgColor="#000000" fontSize="10">
    <math optimize="2" decimalPlaces="4" exponentialThreshold="5">
      <input>
        <e type="operand">φ</e>
        <e type="function" args="1">F</e>
        <e type="operand">1</e>
        <e type="operand">1</e>
        <e type="operand">ε</e>
        <e type="function" preserve="true" args="1">sin</e>
        <e type="bracket">(</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operand">u</e>
        <e type="function" preserve="true" args="1">sin</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>
        <e type="function" preserve="true" args="1">sqrt</e>
        <e type="operator" args="2">/</e>
        <e type="operand">u</e>
        <e type="operand">0</e>
        <e type="operand">φ</e>
        <e type="function" preserve="true" args="4">int</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="5" left="396" top="387" width="323" height="40" color="#0000ff" bgColor="#000000" fontSize="10">
    <text lang="eng">
      <p>the φ in this equation is the from theprevious one</p>
    </text>
  </region>
  <region id="6" left="396" top="459" width="217" height="62" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">x</e>
        <e type="function" args="1">c</e>
        <e type="operand">1</e>
        <e type="operand">0</e>
        <e type="operand">x</e>
        <e type="operator" args="2">≤</e>
        <e type="bracket">(</e>
        <e type="operand">x</e>
        <e type="operand">π</e>
        <e type="operand">2</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">≤</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">&amp;</e>
        <e type="operand" style="string" />
        <e type="function" preserve="true" args="3">cases</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="7" left="81" top="468" width="273" height="39" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">a</e>
        <e type="operand">ε</e>
        <e type="function" preserve="true" args="1">sin</e>
        <e type="bracket">(</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">:</e>
      </input>
      <result action="numeric">
        <e type="operand">0.997557136273092</e>
      </result>
    </math>
  </region>
  <region id="8" left="81" top="522" width="205" height="187" color="#0000ff" bgColor="#000000" fontSize="10" showInputData="False">
    <plot type="2d" render="lines" scale_x="5.39478220936421" scale_y="14.8574291628039" scale_z="80.1525945243837" rotate_x="0" rotate_y="0" rotate_z="0" transpose_x="-81" transpose_y="-66" transpose_z="0">
      <description active="true" position="Top" lang="eng">
        <p>Nonintegrable singularity of the integrand in the integration interval:</p>
      </description>
      <input>
        <e type="operand">x</e>
        <e type="function" args="1">F</e>
        <e type="operand">x</e>
        <e type="function" args="1">c</e>
        <e type="operator" args="2">*</e>
        <e type="operand">π</e>
        <e type="operand">2</e>
        <e type="operator" args="2">/</e>
        <e type="operand">10</e>
        <e type="operand">π</e>
        <e type="operand">2</e>
        <e type="operator" args="2">/</e>
        <e type="operand">2</e>
        <e type="operator" args="1">-</e>
        <e type="operand">2</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="6">mat</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">sys</e>
      </input>
    </plot>
  </region>
  <region id="9" left="342" top="522" width="174" height="56" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">u</e>
        <e type="function" args="1">f</e>
        <e type="operand">1</e>
        <e type="operand">1</e>
        <e type="operand">a</e>
        <e type="operand">u</e>
        <e type="function" preserve="true" args="1">sin</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>
        <e type="function" preserve="true" args="1">sqrt</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="10" left="333" top="576" width="240" height="187" color="#000000" bgColor="#ffffff" fontSize="10" showInputData="False">
    <plot type="2d" render="lines" scale_x="1" scale_y="4.54902325649365" scale_z="4.54902325649365" rotate_x="0" rotate_y="0" rotate_z="0" transpose_x="0" transpose_y="0" transpose_z="0">
      <input>
        <e type="operand">x</e>
        <e type="function" args="1">f</e>
        <e type="operand">π</e>
        <e type="operand">2</e>
        <e type="operator" args="2">/</e>
        <e type="operand">10</e>
        <e type="operand">π</e>
        <e type="operand">2</e>
        <e type="operator" args="2">/</e>
        <e type="operand">2</e>
        <e type="operator" args="1">-</e>
        <e type="operand">2</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="6">mat</e>
        <e type="operand">0</e>
        <e type="operand">a</e>
        <e type="operand" style="string">+</e>
        <e type="operand">100</e>
        <e type="operand" style="string">red</e>
        <e type="operand">1</e>
        <e type="operand">5</e>
        <e type="function" preserve="true" args="7">mat</e>
        <e type="operand">3</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="5">sys</e>
      </input>
    </plot>
  </region>
  <region id="11" left="27" top="792" width="174" height="56" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">u</e>
        <e type="function" args="1">f</e>
        <e type="operand">1</e>
        <e type="operand">1</e>
        <e type="operand">b</e>
        <e type="operand">u</e>
        <e type="function" preserve="true" args="1">sin</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>
        <e type="function" preserve="true" args="1">sqrt</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="12" left="27" top="846" width="405" height="57" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="4">
      <input>
        <e type="operand">u</e>
        <e type="function" args="1">f</e>
        <e type="operand">u</e>
        <e type="function" args="2">int</e>
        <e type="function" preserve="true" args="1">maple</e>
      </input>
      <result action="symbolic">
        <e type="operand">u</e>
        <e type="function" preserve="true" args="1">cos</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="function" preserve="true" args="1">sqrt</e>
        <e type="operand">u</e>
        <e type="function" preserve="true" args="1">sin</e>
        <e type="operand">b</e>
        <e type="function" preserve="true" args="1">sqrt</e>
        <e type="function" args="2">EllipticF</e>
        <e type="operator" args="2">*</e>
        <e type="operand">u</e>
        <e type="function" preserve="true" args="1">cos</e>
        <e type="operator" args="2">/</e>
      </result>
    </math>
  </region>
</regions>