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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "int((1+sin(t))/(3+co
s(t)),t=0..2*Pi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*(\"\"#!\"\"F%#
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fy((1+(z-1/z)/2/I)/(3+(z+1/z)/2)/I/z);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#**,(*&\"\"#\"\"\"%\"zGF'!\"\"*&)F(F&F'^#F'F'F'^#F)F'F'F(F),(*&\"
\"'F'F(F'F'*$F+F'F'F'F'F)F,F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 21 "ro:=solve(z^2+6*z+1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#roG6
$,&\"\"$!\"\"*&\"\"#\"\"\"F*#F+F*F+,&F'F(*&F*F+F*F,F(" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "evalf(ro);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6$$!*wGdr\"!\"*$!+CrUGeF%" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 69 "r1:=limit((z-ro[1])*(2*z-I*z^2+I)/(z^2+6*z+1)/I/z,z=r
o[1]): evalc(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&,&*&\"\")\"\"
\"\"\"##F(F)!\"\"\"#7F(F(,&*&F'F(F)F*F(F,F+F+F(*(,&*&\"\"$F(F)F*F(\"\"
%F+F(F-F+^#F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "r0:=ev
al((2*z-I*z^2+I)/(z^2+6*z+1)/I,z=0); " }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#>%#r0G\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "simplify
(2*Pi*I*(r1+r0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$**\"\"#!\"\"%#P
iG\"\"\",&*&\"\"$F(F%#F(F%F(\"\"%F&F(,&F+F&*&F%F(F%F,F(F&F&" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "expand((3-2*sqrt(2))*(3+2*sq
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"> " 0 "" {MPLTEXT 1 0 37 "expand((-4+3*sqrt(2))*(3+2*sqrt(2)));" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#*$\"\"##\"\"\"F$" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 53 "int((1-x+x^2)/(1-2*x+3*x^2)^2,x=-infinity..in
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\"\"##F&F)%#PiGF&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "ro:=
solve(1-2*x+3*x^2,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#roG6$,&#\"
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "res:=limit(diff((z-ro[1])^2*(1-z+z^
2)/(1-2*z+3*z^2)^2,z),z=ro[1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$
resG*&^##!\"$\"#;\"\"\"\"\"##F*F+" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 18 "evalc(2*Pi*I*res);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#,$**\"\"$\"\"\"\"\")!\"\"\"\"##F&F)%#PiGF&F&" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 52 "int(cos(2*x)/(1-2*x+3*x^2)^2,x=-infinity..infini
ty);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,2**^##\"\"$\"#;\"\"\"\"\"##F)
F*%#PiGF)-%$sinG6#,&#F*F'F)*&^#F1F)F*F+F)F)F)*&F&F)*(F*F+F,F)-%$cosGF/
F)F)F)**^##!\"$F(F)F*F+F,F)-F.6#,&F1F)*&^##!\"#F'F)F*F+F)F)F)*&F&F)*(F
*F+F,F)-F7F=F)F)F)*&#F)\"\"%F)*&F,F)F6F)F)F)*(^#FGF)F,F)F-F)F)*&FGF)*&
F,F)FEF)F)F)*(^##!\"\"FHF)F,F)F<F)F)" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 9 "evalf(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+bz**3
**!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "res:=limit(diff((z
-ro[1])^2*exp(2*z*I)/(1-2*z+3*z^2)^2,z),z=ro[1]);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%$resG,$*&#\"\"\"\"#;F(*&,&*(^#!\"$F(\"\"##F(F/)!\"\",
$*(F/F(\"\"$F2%#PiGF2F(F(F(*&^#!\"%F(F1F(F(F(-%$expG6#*$F/F0#!\"#F5F(F
(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "Re(evalc(2*Pi*I*res));
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&#\"\"\"\"\")F&*(%#PiGF&,&*(\"
\"$F&\"\"##F&F--%$cosG6##F-F,F&!\"\"*&\"\"%F&F/F&F3F&-%$expG6#*$F-F.#!
\"#F,F&F3" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+ez**3**!#5" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 46 "int((sin(t)^2-2*cos(t))/(2+cos(t)),t=0..2*Pi);
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#F&F%F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "f:=(((z-1/z)/2/I
)^2-2*(z+1/z)/2)/(2+(z+1/z)/2)/z/I: simplify(%);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#**^##\"\"\"\"\"#F&,,*$)%\"zG\"\"%F&F&*&F'F&)F+F'F&!\"\"
F&F&*&F,F&)F+\"\"$F&F&*&F,F&F+F&F&F&F+!\"#,(*&F,F&F+F&F&*$F.F&F&F&F&F/
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "ro:=solve(z^2+4*z+1);" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#roG6$,&\"\"#!\"\"*$\"\"$#\"\"\"F'
F,,&F'F(F)F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6$$!*#>\\zE!\"*$!+330KPF%" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "limit(f*z,z=0);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#%*undefinedG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 31 "res1:=limit(diff(f*z^2,z),z=0);" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#>%%res1G\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "res2:=l
imit(f*(z-ro[1]),z=ro[1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%res2G
*&,&^#!#7\"\"\"*&^#\"\"(F)\"\"$#F)\"\"#F)F),&\"#@!\"\"*&\"#7F)F-F.F)F2
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "evalc(2*Pi*I*res2);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,$**\"\"#\"\"\"%#PiGF&,&\"#7!\"\"*&\"
\"(F&\"\"$#F&F%F&F&,&\"#@F**&F)F&F-F.F&F*F*" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 40 "expand((21+12*sqrt(3))*(21-12*sqrt(3)));" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#\"\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 39 "expand((7*sqrt(3)-12)*(21+12*sqrt(3)));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,$*&\"\"$\"\"\"F%#F&\"\"#F&" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 47 "f:=(z^2-3*I*z+4)/(z^3-(3+I)*z^2+(2-I)*z+8-3*I):" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "ro:=solve(z^3-(3+I)*z^2+(2-
I)*z+8-3*I,z):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "seq(evalf
(abs(ro[i]-(3-2*I))),i=1..3);   # radius 2" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6%$\"+#\\#\\EU!\"*$\"+E+/K<F%$\"+\\p0MZF%" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "limit((z-ro[2])*f,z=ro[2]):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "evalf(2*Pi*I*%);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#^$$!+!y,AC$!\"*$\"+TF#Hl#F&" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "int(1/(x^4-8*x^3+42*x^2-104*x+169)^
2,x=-infinity..infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*(\"\"&
\"\"\"\"&#*\\$!\"\"%#PiGF&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 40 "ro:=solve(z^4-8*z^3+42*z^2-104*z+169,z);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#roG6&^$\"\"#\"\"$^$F'!\"$F&F)" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 72 "limit(diff((z-2-3*I)^4/(z^4-8*z^3+42*z^2-104*z
+169)^2,z,z,z),z=2+3*I)/6;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#^##!\"&
\"&%)*p" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "2*Pi*I*%;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*(\"\"&\"\"\"\"&#*\\$!\"\"%#PiGF&F&
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