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React to console inputs (commands) - how to handle multiple options most efficient?

Some information (don't want to confuse you with a lot of shitty code):
I've done a pretty large console programm (my largest project so far) which helps me a lot with managing some accounts / assets and more. I'm constantly adding more features but at the same time I reshape the code to work on my shitty coding style.
The console program has a lot of commands the user can type and for every command different methods get called / objects get created / manipulated and so on.
My keywords which are saved in an ArrayList<String> and my commands have this type: [keyword] [...n more Strings]
DESIGN PROBLEM 1:
I have a method cmdProcessor(String[] arguments) which handles the input (command) of the user, and the [keyword] is always the first argument arguments[0]. That means I have a large number of if-statements of this type:
if(arguments[0].equalsIgnoreCase("keyword") callMethod(argmts); where in the String[] argmts the remaining arguments[1] ... [n] are.
Is this a good way to handle this or should I go with switch-case?
Or something else (what?)? Is it better to save the keywords in a HashMap<String, Method>?
DESIGN PROBLEM 2:
The methods (see above callMethod(argmts) ), which are triggered by the entered keyword look even more chaotic. Since the same method can have different numbers and forms of arguments saved in the String[] argmts the method is full of if(argmts.length == ...) to check length, and every of these if-blocks has a bunch of switch-case options which also have a lot of ifs and so on. The last else and the default-case in switch-case I always use for error-handling (throwing error codes and and explanation why the pattern doesn't match and so on).
Is this good or are there better ways?
I thought about using lots of submethods, which would also blow up
my program and cost a lot of time but maybe improve readability / overview. Is this okay, or what is the best
option in such cases (lots of ifs and switch-case)?
Since I want to build more and more around this program maybe I should start now to fix bad design before it's too late. :)

About Design-Problem 1:
My go-to would be to register a lot of Handlers, which you can base on a common interface and then implement the specific behavior individually. This is good, because the central method handling your input is slim, and you only need to register a lot of singletons once, on initialization. Disadvantage: if you forget one, it will not work. So maybe, you can register them automatically (reflection or something thelike).
Aside from that, a map is better than a List in this case, because (I assume) you don't need a sorting. You need a mapping from key to behavior, so a map seems better (though even a very large set of keywords would probably not be very inefficient, if you stick to a list).
About Design Problem 2:
If I was you, I'd use actual Regular-Expression patterns. Take a look at the java.util.regex.Pattern-class. You can isolate groups and validate the values you receive. Though it does not spare you the exception/error-handling, it does help a lot in segmentation and interpretation efforts.

How to calculate max value of function in range?

I have some function (for example, double function(double value)), and some range (for example, from A to B). I need to calculate max value of function in this range. Are there existed libraries for it? Please, give me advice.

If the function needs to handle floating-point values, you're going to have to use something like Golden section search. Note that for this specific method, there are significant limitations regarding the functions that can be handled (specifically it must be unimodal). There are some adjustments you can make to the algorithm which extend it to more functions, specifically these modifications will allow it to work for continuous functions.

Is this a continuous function, or a set of discrete values? If discrete values, then you can either iterate over all values, and set max/min flags as 808sound suggests, or you can load all values into an array.
If it's a continuous function, then you can either populate an array with the function's value at discrete inputs, and find the max as above, or if it's differentiable, then you can use basic calculus to find the points at which df(x)/dx are 0. The latter case is a little more abstract, and probably more complicated than you want, though?
A quick google search led me to this:
http://code.google.com/p/javacalculus/
But I've never used it myself, so I don't know if that implements the required functionality. It does differential equations, though, so I assume they'd have "baby stuff" like basic differentiation.

I do not know if there are any librairies in Java for your problem.
But I know you can easily do that with MatLab (or Octave for the OpenSource equivalent).

If you do not have any indication of what the functions inner workings are (i.e. the function is a black box that accepts an input and produces an output), there is no "easy" way to find the global maximum.
There are an infinite number of points to choose for your input (technically) so "iterating over all possible inputs" is not feasible mathematically.
There are various algorithms that will give you estimated maximum values ina function like this:
The hill climbing algorithm, and the firefly algorithm are two, but there are many more. This is a fairly well documented/studied computer science problem and there is a lot of material online for you to look at. I suggest starting with the hill climbing algorithm, and maybe expanding out to other global optimization algorithms.
Note: These algorithms do not guarantee that the result is the maximum, but provide an estimate of its value.*

Most Efficient way to calculate integrals/derivatives of inputted functions in Java?

I now have an idea, that I use the function as a string, and I calculate the real integral by hand, and ask a question to the user what the definite integral is, but that isn't a real solution.
I was wondering if there was a way to input a function and output an integral/derivative (depending on user choice). My initial step was to put it into an array somehow, but given the many types of functions, this wasn't happening.
I researched everywhere, and I haven't found a method that actually does this with no additional code, nor any code that actually does this, period.
Also, I want to see if there was a way to make a GUI interface and plot inputted functions on to that, if that's possible too.
Thanks :)

What you're describing is known as symbolic integration. There's currently no fully general way to implement it, but there are some techniques available. One such is the Risch algorithm.
Alternatively, an easier problem than symbolic integration is [symbolic differentiation -- and, if the differential of the user's input is equivalent* to the expression which they were asked to integrate, then their integral is probably correct.
You may also want to consider using an existing CAS**, such as Mathematica, to implement this. They've already implemented most of the tools you're after.
*: Keep in mind, though, that two mathematical expressions may be equivalent without being identical, either in trivial ways (e.g, terms in a different order), more complex ones (e.g, large expressions factored differently), or fundamentally (e.g, trig functions replaced with complex exponentials or vice versa).
**: Computer algebra system

Javacalculus is what you are looking for.
Good luck!

Measure input coverage in Java test cases

Is it possible to measure how many distinct inputs were passed on to the methods of a class under test from existing test cases.
I'd like to measure something like code coverage, but for inputs instead.

I don't know of any COTS tools that compute input coverage, so I'd expect you to have to build a tool that did what you wanted.
My technical paper Branch Coverage for Arbitrary Languages Made Easy describes an approach for building test coverage tools for arbitrary languages using a Program transformation system to insert arbitrary probes into source code.
The paper is naturally focused on building code coverage, but the probe insertion technique is general and you can decide where to place probes and what they do. In your case, you want to place probes only at method entry, and you want the probes to track the input argument instances. The paper shows how to place probes anywhere by using a source code pattern to indicate the point of insertion; method entry is easy to describe as a pattern.
Capturing the input instances is more awkward but doable. You'll have to decide what an "input" is; is it just the argument values, or some kind of deep copy of the arguments? Likely what you need to do is create (per-method instrumented) an object type whose data members corresponds to the parameters, instantiate such an object with a copy (to appropriate depth) of the arguments, and store that object in a per-method hash table. (The transforamtion rules can insert all this once you know what you want to do as a code idiom). With all that, at execution, your hash table builds up the argument set, which is the key to what you want.
You can (continuously) count unique argument-set instances by controlling what happens when you insert duplicates into the hash table; that count (per method) can be managed in a global array that is exported at program completion. The paper discusses such a global array, and the various ways to export/display it in general.
Our line of test coverage and profilers are built using the techniques in the paper. The profilers keep counts/times in such global arrays (essentially what you need) and export them to a display engine that draws heat histograms, showing where the hot spots are. Those display engines are language and probe-data-source agnostic off-the-shelf in that they come in any of our (profiler) tools, including the Java profiler, so you could press one of them into service for the display task.

Is there a library similar to PyCogent, but in Java (or Scala)?

I'm writing a biological evolution simulator. Currently, all of my code is written in Python. For the most part, this is great and everything works sufficiently well. However, there are two steps in the process which take a long time and which I'd like to rewrite in Scala.
The first problem area is sequence evolution. Imagine you're given a phylogenetic tree which relates a large set of proteins. The length of each branch represents the evolutionary distance between the parent and child. The root of the tree is seeded with a single sequence, and then an evolutionary model (e.g. http://en.wikipedia.org/wiki/Models_of_DNA_evolution) is used to evolve the sequence along the tree structure; taking into account the branch lengths. PyCogent takes a long time to perform this step, and I believe that a reasonable Java/Scala implementation would be significantly faster. Do you know of any libraries that implement this type of functionality. I want to write the application in Scala, so, due to interoperability, any Java library will suffice.
The second problem area is the comparison of the generated sequences. The problem is, given a set of sequences for the proteins in a number of different extant species, attempt to use the sequence to reconstruct the phylogenetic tree which relates the species. This problem is inherently computationally demanding, because one must basically do a pairwise comparison between all sequences in the extant species. Here again, however, I feel like a Java/Scala implementation would perform significantly faster than a Python one, if for nothing else than the unfortunately slow speed of looping in Python. This part I could write from scratch more easily than the sequence evolution part, but I'd be willing to use a library for it as well if a good one exists.
Thanks,
Rob

For the second problem, why not make use an existing program for comparing sequences and infering phylogenetic trees, like RAxML or MrBayes and call that? Maximum likelihood and Bayesian inference are very sophisticated models for these problems, and using them seems a far better idea than implementing it yourself - something like a maximum parsiomony or a neihbour-joining tree, which probably could be written from scratch for such a project, is not sufficient for evolutionary analysis. Unless you just want a very quick and dirty topology (and trees inferred via MP or NJ are really often quite false), where you can probably use something like this