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    <identity>
      <id>3d6c0455-6df8-4b91-bc37-b9179b8e11aa</id>
      <revision>7</revision>
    </identity>
    <metadata lang="eng">
      <author>overlord</author>
    </metadata>
    <calculation>
      <precision>3</precision>
      <exponentialThreshold>5</exponentialThreshold>
      <trailingZeros>false</trailingZeros>
      <significantDigitsMode>false</significantDigitsMode>
      <roundingMode>0</roundingMode>
      <approximateEqualAccuracy>0</approximateEqualAccuracy>
      <fractions>decimal</fractions>
    </calculation>
    <pageModel active="false" viewMode="1" printGrid="false" printAreas="true" simpleEqualsOnly="false" printBackgroundImages="true">
      <paper id="9" orientation="Portrait" width="827" height="1169" />
      <margins left="39" right="39" top="49" bottom="49" />
      <header alignment="Center" color="#a9a9a9">&amp;[DATE] &amp;[TIME] - &amp;[FILENAME]</header>
      <footer alignment="Center" color="#a9a9a9">&amp;[PAGENUM] / &amp;[COUNT]</footer>
      <backgrounds />
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  <regions type="content">
    <region left="36" top="9" width="355" height="26" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">restart</e>
          <e type="function" args="1">MaximaControl</e>
        </input>
        <result action="numeric">
          <e type="operand" style="string">Restart complete.</e>
        </result>
      </math>
    </region>
    <region left="36" top="36" width="570" height="86" color="#000000" fontSize="10">
      <math decimalPlaces="4">
        <input>
          <e type="operand">0.85</e>
          <e type="operand">1</e>
          <e type="operand">1</e>
          <e type="operand">x</e>
          <e type="operand">ε.co</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">-</e>
          <e type="bracket">(</e>
          <e type="operand">n</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">x</e>
          <e type="operand">0</e>
          <e type="operand">ε.co</e>
          <e type="function" args="4">int</e>
          <e type="function" args="1">Maxima</e>
        </input>
        <result action="none">
          <e type="operand" style="string">n is assumed to be positive.</e>
          <e type="operand" style="string">ε_%_co is assumed to be positive.</e>
          <e type="operand">0.85</e>
          <e type="operand">n</e>
          <e type="operator" args="2">*</e>
          <e type="operand">ε.co</e>
          <e type="operator" args="2">*</e>
          <e type="operand">n</e>
          <e type="operand">1</e>
          <e type="operator" args="2">+</e>
          <e type="operator" args="2">/</e>
          <e type="operand">3</e>
          <e type="operand">1</e>
          <e type="function" args="5">sys</e>
        </result>
      </math>
    </region>
    <region left="639" top="54" width="91" height="23" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Arial" fontSize="10">
        <content>
          <p>correct result</p>
        </content>
      </text>
    </region>
    <region left="702" top="54" width="20" height="24" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">ε</e>
        </input>
      </math>
    </region>
    <region left="27" top="126" width="580" height="100" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">0.85</e>
          <e type="operand">1</e>
          <e type="operand">1</e>
          <e type="operand">x</e>
          <e type="operand">ε.co</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">-</e>
          <e type="bracket">(</e>
          <e type="operand">n</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">x</e>
          <e type="operand">0</e>
          <e type="operand">ε.co</e>
          <e type="function" args="4">Int</e>
        </input>
        <result action="none">
          <e type="operand" style="string">n is assumed to be positive.</e>
          <e type="operand" style="string">ε_%_co is assumed to be positive.</e>
          <e type="operand">17</e>
          <e type="operand">ε.co</e>
          <e type="operand">n</e>
          <e type="operand">1</e>
          <e type="operator" args="2">+</e>
          <e type="operator" args="2">^</e>
          <e type="operand">n</e>
          <e type="operator" args="1">-</e>
          <e type="operand">1</e>
          <e type="operator" args="2">-</e>
          <e type="bracket">(</e>
          <e type="operand">ε.co</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">20</e>
          <e type="operand">n</e>
          <e type="operand">1</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="1">-</e>
          <e type="operand">3</e>
          <e type="operand">1</e>
          <e type="function" args="5">sys</e>
        </result>
      </math>
    </region>
    <region left="639" top="144" width="101" height="23" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Arial" fontSize="10">
        <content>
          <p>incorrect result</p>
        </content>
      </text>
    </region>
    <region left="27" top="225" width="379" height="26" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">int</e>
          <e type="function" args="1">MaximaTakeover</e>
        </input>
        <result action="numeric">
          <e type="operand" style="string">int() handled by Maxima</e>
        </result>
      </math>
    </region>
    <region left="27" top="261" width="513" height="100" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">0.85</e>
          <e type="operand">1</e>
          <e type="operand">1</e>
          <e type="operand">x</e>
          <e type="operand">ε.co</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">-</e>
          <e type="bracket">(</e>
          <e type="operand">n</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">x</e>
          <e type="operand">0</e>
          <e type="operand">ε.co</e>
          <e type="function" args="4">int</e>
        </input>
        <result action="none">
          <e type="operand" style="string">n is assumed to be positive.</e>
          <e type="operand" style="string">ε_%_co is assumed to be positive.</e>
          <e type="operand">17</e>
          <e type="operand">ε.co</e>
          <e type="operand">n</e>
          <e type="operand">1</e>
          <e type="operator" args="2">+</e>
          <e type="operator" args="2">^</e>
          <e type="operand">n</e>
          <e type="operator" args="1">-</e>
          <e type="operand">1</e>
          <e type="operator" args="2">-</e>
          <e type="bracket">(</e>
          <e type="operand">ε.co</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">20</e>
          <e type="operand">n</e>
          <e type="operand">1</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="1">-</e>
          <e type="operand">3</e>
          <e type="operand">1</e>
          <e type="function" args="5">sys</e>
        </result>
      </math>
    </region>
    <region left="36" top="360" width="296" height="51" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">ε.co</e>
          <e type="operand">0</e>
          <e type="operator" args="2">&gt;</e>
          <e type="operand">n</e>
          <e type="operand">0</e>
          <e type="operator" args="2">&gt;</e>
          <e type="function" args="2">assume</e>
          <e type="function" args="1">Maxima</e>
        </input>
        <result action="symbolic">
          <e type="operand">ε.co</e>
          <e type="operand">0</e>
          <e type="operator" args="2">&gt;</e>
          <e type="operand">n</e>
          <e type="operand">0</e>
          <e type="operator" args="2">&gt;</e>
          <e type="operand">2</e>
          <e type="operand">1</e>
          <e type="function" args="4">sys</e>
        </result>
      </math>
    </region>
    <region left="27" top="423" width="299" height="75" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">0.85</e>
          <e type="operand">1</e>
          <e type="operand">1</e>
          <e type="operand">x</e>
          <e type="operand">ε.co</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">-</e>
          <e type="bracket">(</e>
          <e type="operand">n</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">x</e>
          <e type="operand">0</e>
          <e type="operand">ε.co</e>
          <e type="function" args="4">int</e>
        </input>
        <result action="none">
          <e type="operand">17</e>
          <e type="operand">n</e>
          <e type="operator" args="2">*</e>
          <e type="operand">ε.co</e>
          <e type="operator" args="2">*</e>
          <e type="operand">20</e>
          <e type="operand">n</e>
          <e type="operand">1</e>
          <e type="operator" args="2">+</e>
          <e type="bracket">(</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">/</e>
        </result>
      </math>
    </region>
    <region left="18" top="558" width="1330" height="764" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand" style="string">all</e>
          <e type="function" args="1">MaximaLog</e>
        </input>
        <result action="numeric">
          <e type="operand" style="string">pid=20208
Maxima 5.44.0 http://maxima.sourceforge.net
using Lisp SBCL 2.0.0
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
(%i1) display2d:false$
(%i2) linel:700$
(%i3) simpsum:true$
(%i4) logsimp:true$
(%i5) keepfloat:true$
(%i6) ratprint:false$
(%i7) load(vect)$
(%i8) load(abs_integrate)$
WARNING: redefining MAXIMA::OPAPPLY in DEFMACRO
WARNING: redefining MAXIMA::OPCONS in DEFMACRO
(%i9) setup_autoload(mnewton, mnewton)$
(%i10) setup_autoload(draw, draw2d, draw3d)$
(%i11) load(lsquares)$
(%i12) logb(x,y):=log(x)/log(y)$
(%i13) ntewurzel(x,n):=x^(1/n)$
(%i14) el(x,y):=x[y]$
(%i15) el(x,[y]):=if equal(length(y),1) then x[y[1]] else x[y[1],y[2]]$
(%i16) Fit(Data,vars,fun,par,init):=lsquares_estimates_approximate(lsquares_mse(Data,vars,fun),par,initial=init,iprint=[-1,0])$
(%i17) Fit6(Data,vars,fun,par,init,t):=lsquares_estimates_approximate(lsquares_mse(Data,vars,fun),par,initial=init,tol=float(t),iprint=[-1,0])[1]$
(%i18) Residuals(Data,vars,fun,[par]):=float(transpose(matrix(lsquares_residuals(Data,vars,fun,par))))$
(%i19) MSE(Data,vars,fun,[par]):=float(lsquares_residual_mse(Data,vars,fun,par))$
(%i20) round2(x,n):=round(x*10^n)/10^n$
(%i21) check;
(%o21) check
(%i22) integrate(0.85*(1-(1-x/ε_%_co)^n),x,0,ε_%_co);Is n positive, negative or zero?

positive;Is ε_%_co positive, negative or zero?

positive;(%o22) (0.85*n*ε_%_co)/(n+1)
(%i23) integrate((17*(1-((ε_%_co-x)/ε_%_co)^n))/20,x,0,ε_%_co);Is n positive, negative or zero?

positive;Is ε_%_co positive, negative or zero?

positive;(%o23) -(17*(ε_%_co^(n+1)+((-n)-1)*ε_%_co))/(20*(n+1))
(%i24) integrate((17*(1-((ε_%_co-x)/ε_%_co)^n))/20,x,0,ε_%_co);Is n positive, negative or zero?

positive;Is ε_%_co positive, negative or zero?

positive;(%o24) -(17*(ε_%_co^(n+1)+((-n)-1)*ε_%_co))/(20*(n+1))
(%i25) assume(ε_%_co&gt;0,n&gt;0);
(%o25) [ε_%_co &gt; 0,n &gt; 0]
(%i26) integrate((17*(1-((ε_%_co-x)/ε_%_co)^n))/20,x,0,ε_%_co);
(%o26) (17*n*ε_%_co)/(20*(n+1))
(%i27) </e>
        </result>
      </math>
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