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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "dot:=proc(r,q);simpl
ify(add(r[i]*q[i],i=1..3)) end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 83 "cross:=proc(r,q);[r[2]*q[3]-r[3]*q[2],r[3]*q[1]-r[1]*q[3],r[1]
*q[2]-r[2]*q[1]] end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "ma
g:=proc(q);sqrt(add(q[i]^2,i=1..3))end:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 52 "plugin:=proc(g,r);eval(g,\{x=r[1],y=r[2],z=r[3]\})end
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{TEXT -1 4 "Q14:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 72 "r:=[2*cos(u),3*sin(u),v]:   simplify(9*r[1]^2+4*r[2]^
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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "cross(diff(r,u),diff(r,v));
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Q18:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 79 "
r:=[v*cos(u),v*sin(u)/2,v]:   simplify(r[1]^2+4*r[2]^2-r[3]^2);  #just
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"> " 0 "" {MPLTEXT 1 0 40 "cross(diff(r,u),diff(r,v)): simplify(%);" }
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{MPLTEXT 1 0 36 "F:=[x^2,exp(y),1]:   r:=[u,v,1-u-v]:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "int(int(dot(plugin(F,r),cross(diff(
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r,v))),u=0..Pi/2),v=0..h);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*(\"#<
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0 71 "int(int(plugin(G,r)*mag(cross(diff(r,u),diff(r,v))),u=0..1-v),v=
0..1.);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+r+!32\"!\"*" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 4 "Q16:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 48 "G:=(x^2+y^2)^2-z^2:  r:=[u*cos(v),u*sin(v
),2*u]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "int(int(plugin(G
,r)*mag(cross(diff(r,u),diff(r,v))),u=0..1),v=-Pi..Pi);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#,$**\"\"&\"\"\"\"\"$!\"\"F%#F&\"\"#%#PiGF&F(" }}
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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "G:=y^2+(z-h/2)^2:     r:=[co
s(u),sin(u),v]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "int(int(
plugin(G,r)*mag(cross(diff(r,u),diff(r,v))),u=0..2*Pi),v=0..h);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&%\"hG\"\"\"%#PiGF&F&*&#F&\"\"'F&*&
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