{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 256 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 257 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 258 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 261 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 264 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 265 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 266 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 267 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 268 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 269 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 270 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 271 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 272 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 273 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 274 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 275 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 276 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Outpu t" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 256 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 257 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 258 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 259 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 260 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 261 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT -1 60 "MAT 155 Project I Fall 2 002" }}{PARA 257 "" 0 "" {TEXT -1 44 " Introduct ion to Maple" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 256 17 "Saving this file:" }}{PARA 0 "" 0 "" {TEXT -1 54 "Before you begin working you should save this file as " }{TEXT 259 14 "yourn ame1.mws " }{TEXT -1 76 "by selecting \"File\" on the far left of the \+ top bar of Maple V and choosing \"" }{TEXT 257 7 "Save As" }{TEXT -1 171 "\". A window will appear and you will fill in the file name. Y ou should regularly save this file using the \"Save As\". You should also save the file with a second name " }{TEXT 260 15 "yourname1b.mws " }{TEXT -1 20 "using the \"Save As\" " }{TEXT 261 26 "so that you ha ve a backup " }{TEXT -1 402 "in case your file is damaged. The comput er will tell you that the file already exists and you will click on \" Yes\" that you agree to overwrite it. If you just use the \"Save\" in stead of the \"Save As\" then the file will be saved with whichever na me is on the top bar of this window. Be careful to check that you only have one file window open or you may have different files saving on t op of each other." }}}{PARA 0 "" 0 "" {TEXT -1 1 " " }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 1 " " }{MPLTEXT 1 0 0 "" }{TEXT 258 38 "Put your name on the top of this file " }{TEXT -1 111 "by clicking your mouse right below the title and then typing your name. Then return here using th e down arrow." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 1 " " }}}{EXCHG {PARA 258 "" 0 "" {TEXT -1 21 "Problem 1. \+ Operations" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 304 "Recall that multiplication, addition, division, etc are all operation s. To use Maple as a calculator, you just type the formula you are in terested, then type a semicolin ( ; ) and then hit enter. Maple obeys the order of operations so it will do exponents first, then multimpli cation and division, then" }}{PARA 0 "" 0 "" {TEXT -1 95 "addition and subtraction. If you want it to do addition first, you must put it in parenthesis." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 61 "Click on the following lines and hit \"Enter\" to see exa mples:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "1+2*3;" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "(1+2)*3;" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "6-4/2;" }{TEXT -1 0 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "(6-4)/2;" }{TEXT -1 0 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "3^2;" }{TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "3*2^2;" }{TEXT -1 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 220 "Now type compute the following us ing maple yourself. You must type your command on a line beginning wi th a [> symbol which is called a prompt. Don't forget the ; or Maple \+ will write : \"Warning, premature end of input\"." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 18 "a) (3+4) cubed." } {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 5 "b) " }{TEXT 264 7 " 1+15 " }}{PARA 0 "" 0 "" {TEXT -1 67 " 7+1 (the answer is 16/8=2 be careful). \+ " }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 72 "c) 5(3+2) (don't forget the symbol for m ultimplication)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 259 "" 0 " " {TEXT -1 140 "It is time to save your work. Go to the top of the fi le using the up arrow key and review how to do this. Remember you mus t save it twice." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 260 "" 0 "" {TEXT -1 30 "Problem 2: Decimal Expansions" }{MPLTEXT 1 0 0 " " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 168 "Maple always tries to give a n exact answer but if there is no exact answer then it just displays a fraction or a square root. If you want a decimal expansion, use the \+ " }{TEXT 269 6 "evalf " }{TEXT -1 41 "command. Hit enter to see how it works: " }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "1/2;" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "evalf(1/2);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "2^(1/2);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 142 "Re call that the square root of 2 is irrational. So the decimal expansio n continues forever but Maple only gives the first ten decimal places. " }{MPLTEXT 1 0 0 "" }}}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$-%%sqrtG6#\" \"#\"\"\"" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "evalf( 2^(1/2)) ;" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 121 "Remember tha t there is no real square root of (-1). There is an imaginary square \+ root for (-1) which is called i or I. " }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "(-1)^(1/2);" }{TEXT -1 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 87 "In Calculus I we do not use imagin ary or complex numbers. So be careful if you get an " }{TEXT 273 1 "I " }{TEXT -1 14 " in an answer." }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 39 "a) Find the decimal expansion for 1/3." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 28 "b) Find the cube root o f 8." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 28 "c) Find th e cube root of 2." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 1 " " }{MPLTEXT 1 0 0 "" }{TEXT 275 140 "It is time to save your wo rk. Go to the top of the file using the up arrow key and review how t o do this. Remember you must save it twice." }}}{EXCHG {PARA 0 "" 0 " " {TEXT 271 21 "Problem 3: Functions" }}{PARA 0 "" 0 "" {TEXT -1 155 "A function is a mapping from a domain to a range. For example f(x)=x ^2 maps real numbers to real numbers bigger than or equal to 0. Mathe maticians write:" }}{PARA 0 "" 0 "" {TEXT -1 71 "f: (-infinity, infini ty) -> [0, infinity) and f : x -> x^2 " }}{PARA 0 "" 0 "" {TEXT -1 242 "So f takes -1 to 1, -2 to 4, 3 to 9 and so on. To defin e a function in maple we use a similar notation. To make the right ar row we use a dash (near the letter p on the keyboard) and a greater th an sign (>). Hit enter on the following line:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "f:= x -> x^2;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 100 "Note that there is an equals sign in Maple's notation! In Maple \+ := is always used to define things." }}{PARA 0 "" 0 "" {TEXT -1 38 "No w to evaluate a function, you write:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(5);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "f(-3);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 44 "a) Def ine a function g which maps x to x/3." }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 28 "b) Evaluate g at 7 and at 8." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 94 "Maple has alr eady defined some functions. For example sqrt takes a number to its s quare root:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "sqrt(4);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 54 "c) Ask Maple to find the square roots of 9 and of -9." }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 96 "d) In Calculus we often create new functions from old fu nctions. For example, we might want to" }}{PARA 0 "" 0 "" {TEXT -1 174 "take a number and first map it using f and then map it using g. \+ That is we take x and square it using f to get x^2, and then take x^2 \+ and act g on it to get g(x^2) which is:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "g(x^2);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 40 "This new function is written as g(f(x))." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "g(f(x));" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 120 "If you want to compute g first and then f you use f(g( x)). Compute this by hand and then check your answer using Maple." }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "f(g(x));" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 265 24 "Problem 4: Trigonometry" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 153 "Recall the trig functions sine and cosine. If you do not already know their definitions you should not be taking ca lculus! Speak to your teacher today!" }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 94 "You should recall that sin (30 degree s)=1/2 , sin (60 degrees)= sqrt(3)/2, sin (90 degrees)=1" }}{PARA 0 " " 0 "" {TEXT -1 8 "however " }{TEXT 266 50 "in calculus we do not meas ure angles using degrees" }{TEXT -1 9 "!!! " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "sin(30);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "evalf(sin(30));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 197 "As you see by hitting the above lines that Maple does not compute sin(30) and that even the decimal expansion of sin(30) has nothing to do with .5000000000, in fact it is negative. This is because" }} {PARA 0 "" 0 "" {TEXT -1 12 "in calculus " }{TEXT 267 33 "we use radia ns to measure angles." }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 289 "Ask your teacher to explain radians to you if you do not know what they are. There is a very nice picture with a unit circle \+ that can be drawn on the board. This picture also helps you remember \+ when sine and cosine are positive and negative. You may also read App endix A.3 in the text.." }}}{PARA 11 "" 1 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 190 "For a quick conversion from radians to d egrees just remember that the circumference of a circle of radius 1 in 2Pi and the degrees to go all the way around is 360. So 360 degrees = 2Pi. So" }}{PARA 0 "" 0 "" {TEXT -1 36 "90 degrees= 90 (2Pi/360) an d we get:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "90*(2*Pi/360);" } {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 66 "Which is Pi/2 rad ians. So sin (90 degrees)=sin(Pi/2) and we type:" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 10 "sin(Pi/2);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 69 "a) Compute the radians for 60 degrees and then find sin(60 degrees)." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 38 "b) Comp ute the cosine of 180 degrees." }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 72 "c) Find the tangent of Pi/4. Compare it with sin(P i/4) and cos(Pi/4). " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" } {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 33 "d) Notice that cos(Pi/2) is 0 so " }{TEXT 268 26 "tan(Pi/2) is \+ not defined. " }{TEXT -1 26 " See what Maple gives you:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 15 "It should say \"" }{TEXT 274 40 "E rror, (in tan) singularity encountered." }{TEXT -1 126 "\" Maple alw ays tries to explain what is wrong with your command if it asks it to \+ do something impossible or it is not clear." }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 1 " " }}{PARA 261 "" 0 "" {TEXT -1 64 "It is time to save y our work. Remember you must save it twice." }{MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 270 13 "E xploration: " }{TEXT -1 531 "Every project ends with exploration. Bef ore starting the exploration you should make sure that you have comple ted all of the problems. Once you have completed them you can make up similar problems or do recommended exploration problems. If you miss a lab, you must catch up on the previous labs problems to learn all t he commands and ideas that you missed. The exploration need not have \+ been completed to continue with the next project. Your professor may, \+ however, require you to complete the exploration for grading purposes. " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 272 33 "Recommended exploration problems:" }}{PARA 0 "" 0 "" {TEXT -1 91 " To do this work you need only hit enter at the bottom of the lab to cr eate more prompts [>." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 252 "A) Practice using the unit circle to find sin(-Pi), s in(-Pi/2), sin(0), sin(Pi/2), sin(Pi), sin(3Pi/2), sin(2Pi), and chec k your answers with Maple. Then use the unit circle to figure out whe re tangent is undefined and check your answer with Maple. " }}{PARA 0 "" 0 "" {TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 97 "B) Define a fu nction f(x)=1-x^2. Use Maple to study f(sin(x)). Then define a funct ion g(x)=x^2." }}{PARA 0 "" 0 "" {TEXT -1 66 "Use Maple to study g(cos (x)). Compare f(sin(x)) with g(cos(x)). " }{MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 1 " " }{TEXT 276 53 "Remember to save \+ your exploration problems regularly." }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}}{MARK "4 0 3" 111 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }